CP Violation and the CKM Matrix: Assessing the Impact of the Asymmetric B Factories

A. Hocker; F.R. Le Diberder; H. Lacker; J. Charles; J. Malcles; J. Ocariz; L. Roos; M. Pivk; S. Laplace

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CP Violation and the CKM Matrix: Assessing the Impact of the Asymmetric B Factories

J. Charles, A. Hocker, H. Lacker, S. Laplace, F.R. Le Diberder, J. Malcles, J. Ocariz, M. Pivk

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L. Roos

High Energy Physics - Phenomenology · Submitted 17 Jun 2004 · 300 references

Pith's verdict: The standard CKMfitter reference, careful and well documented, with one interpretive sentence that overstates what a 71% goodness-of-fit p-value can support.

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arXiv IDhep-ph/0406184 (version 3)

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CitationA. Hocker, F.R. Le Diberder, H. Lacker, J. Charles, J. Malcles, J. Ocariz, L. Roos, M. Pivk, S. Laplace. "CP Violation and the CKM Matrix: Assessing the Impact of the Asymmetric B Factories." arXiv:hep-ph/0406184 (2004). https://pith.science/paper/IDELGLGJ

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Bottom line: this is the CKMfitter group's second-edition global fit, and it is the reference you will cite for the standard CKM parameter ranges. The fit is careful, the statistical machinery is documented in unusual detail, and the authors are candid about their assumptions. The one place I would push back is the sentence that reads the 71% p-value as strong support for the KM mechanism. What is actually new relative to Ref. [6]: sin 2alpha from B0 -> rho+rho- with isospin discrimination of the penguin, the K+ -> pi+ nu nu constraint from the combined E787/E949 result, an updated QCD-factorization fit to all pi pi and K pi data, and the model-independent New Physics analysis of b->d and b->s gluonic penguins in Part VII. The appendices on the frequentist treatment of Delta m_s and on combining inconsistent measurements are genuine methodological contributions and are worth reading on their own. The fit is well done. Table 1 lists every input with its treatment, the Rfit scheme is spelled out, and the authors state plainly that the scheme rests on a single assumption, namely that the QCD parameters lie inside pre-assigned ranges. They also note in Section II.2.1 that the resulting CL is an upper limit. That is the right caveat. Where I would push: the stress-test's point about the 71% p-value holds. The toy of Section II.3 generates pseudo-data at the best-fit point with Ltheo unmodified, so the p-value is conditional on the QCD parameters sitting at that point. With a dozen bounded nuisance parameters free inside their ranges, chi2_min is small almost by construction, and 71% measures the flexibility of the model rather than the strength of the SM confirmation. The authors' own upper-limit remark covers part of this, but 'strongly supports the KM mechanism' is more than a goodness-of-fit p-value can deliver. It is one sentence, not the fit, and Tables 2 and 3 are unaffected. Minor: the Part IV projections set the branching fraction to the fit's own central value, which is fine as a sensitivity study and clearly labeled, but do not quote those numbers as predictions. The QCD-factorization 'predictions' are post-dictions of the fitted pi pi and K pi data, and the paper says so. Who should read it: anyone who needs a CKM input, and anyone working on the statistical treatment of theory errors in flavor fits. It deserves a serious referee.

Referee report

Significance

This is the reference global CKM analysis of its era and remains a benchmark for how a frequentist flavour fit should be documented. The methodological content is substantial and genuinely reusable: the Rfit scheme with Hat-function treatment of theoretical ranges (Part II.6), the semi-analytic handling of physical boundaries (Section II.2.2.3), the Poisson-correct CL construction for the two-event K+ → π+νν measurement (Section II.2.2), the Δms confidence-level construction of Appendix A, and the measurement-combination scheme of Appendix B. The analysis ships as the public CKMfitter package, so the numbers in Tables 2 and 3 are reproducible rather than asserted, and the paper makes falsifiable projections (Tables 5 and 6 for future K → πνν reaches; Section VI.5 for the ρρ isospin analysis). The paper is also unusually candid about its own assumptions: the range-validity caveat is stated plainly in Section II.1.2, the possible 10% underestimate of charmless branching fractions is flagged in the 'Remark on Radiative Corrections' opening Part VI, and the non-Gaussian cos 2β result is explicitly excluded from the fit in Section III.3.5 rather than quietly absorbed. Those acknowledg(e

Major objections (4)

[III.3.1, Eqs. (73)–(74)] The inference that the 71% p-value 'strongly supports the KM mechanism' is stronger than the statistic warrants, though not for the reason one might first suspect. The toy procedure of Section II.3 does not pin the QCD nuisance parameters at their best-fit values: step 4 explicitly re-minimizes χ² over all ymod in each pseudo-experiment, so the distribution of χ²min does propagate the freedom to move inside the allowed ranges. What is held fixed is the set of ranges themselves, which is the caveat already stated in Section II.1.2. The residual concern is statistical power: with roughly nine observables (Eq. 72) against four CKM parameters plus a comparable number of bounded QCD parameters (fBd√Bd, BK, ξ, mc, mt, ηct, ηB, αS), χ²min is small almost by construction and the toy distribution is concentrated near zero. Please quote the effective number of degrees of freedom used, state explicitly that the p-value is conditional on the ranges of Table 1, and soften 'strongly supports' to something like 'is consistent with' unless a power study is supplied.
[Part VI, 'Remark on Radiative Corrections'; Section VI.2] The authors state that the charmless branching fractions used throughout Part VI may be underestimated by up to 10% because the experimental simulations did not include radiative corrections, and they choose not to correct for it. This systematic is directly load-bearing for the abstract's claim of 'remarkable agreement' of the QCD Factorization fit with the ππ and Kπ data, and for the precise predictions advertised in Section VI.2.3. A sensitivity study is needed: repeat the QCD FA fit of Section VI.2 with B(B0 → π+π−) and B(B0 → K+π−) shifted upward by 10%, and quote the shift in the fitted hadronic parameters, in the goodness of fit, and in the predicted observables. If the agreement survives, say so; if it degrades, the abstract sentence should be qualified.
[III.3.4] The paper reports a p-value of 1.7% (2.4σ, or 1.1% with boundary corrections) for the compatibility of the penguin-dominated sin 2β measurements with the charmonium reference, and then concludes in the abstract that there is 'no unambiguous sign of New Physics'. The reconciliation rests on removing Belle's SφK0S from the all-mode average, which raises the p-value to 29%. That choice is defensible and is stated transparently, but it is consequential enough that the reader should see the full table: the p-value with all experiments, with each experiment removed in turn, and with the boundary-corrected CL. Please also comment on the look-elsewhere effect, since several penguin modes are averaged and one of them is being singled out after the fact.
[III.2.5 and Table 1 (|Vub| average)] The |Vub| input is formed by averaging the inclusive and exclusive central values and assigning the larger of the two theoretical errors, rather than by multiplying the two likelihoods. The motivation (marginal agreement, unsettled theory) is reasonable, but the resulting likelihood is not the product of the two measurements and the quoted |Vub| = (3.90 ± 0.08 ± 0.68) × 10⁻³ therefore carries no information about the tension between the two determinations. Since |Vub| enters the (ρ̄, η̄) constraint directly, please add a cross-check row or appendix entry giving the fit with the product of the two likelihoods, so the reader can see how much of Tables 2 and 3 depends on this conservative choice.

Minor objections (8)

[III.3.5, Eq. (75)] The quoted cos 2β = 2.72 +0.50−0.79 ± 0.27 lies far outside the physical bound |cos 2β| ≤ 1. The text handles this correctly by declining to use the measurement and by warning that a Gaussian interpretation is flawed, but the number and the 89% probability should also be flagged in the figure or table caption where they appear, with the CL definition stated, so that a reader skimming the section does not take 2.72 at face value.
[Part V.1] The sentence 'this tends to overestimates the CL' contains a grammatical error; it should read 'overestimate'.
[Appendix B] The headings 'Psychostatistics' and 'Schizostatistics' are memorable but may not suit the journal's style. Consider neutral section titles with the colloquial names retained in parentheses, so that the methodological content is easy to cite.
[Table 1] The GS/TH asterisk convention is explained in the caption, but the distinction between the asterisk and the dash for the |Vcb| (excl.) row is easy to miss at a glance. A footnote on that row, or a visual separator between the experimental and theoretical blocks, would help.
[Figs. 6, 7 and 8] The text carefully distinguishes (ρ, η) from the phase-convention-invariant (ρ̄, η̄) of Eq. (17), but the figure axis labels drop the bar. Please harmonize the labels with the text, or add a note in each caption stating which convention is plotted.
[IV.2, Eq. (81)] The constant κ+ is defined only by reference to Ref. [180]. For reproducibility of the |Vtd| extraction in Table 5, please quote its numerical value and the associated uncertainty in the text.
[VI.1.2.1, Eqs. (113)–(114)] The two forms of the isospin bound are stated to be equivalent. A one-line demonstration, or a pointer to the equation in Ref. [144] where the equivalence is shown, would save the reader a derivation.
[Figures (general)] The figures are labelled 'Winter 2004'. For the final version, please state the exact data cutoff date in the caption of Fig. 6 or in Section III.2, since several inputs (e.g. the KLOE and KTeV kaon results noted in footnotes 15 and 19) were in flux at the time of writing.

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The paper

The paper claims

The paper argues that a single set of four quark-mixing parameters, fitted jointly to kaon and B-factory data, describes the observed CP violation and mixing, with no unambiguous sign of new physics.

The reading

The paper's aim is to establish that the Cabibbo-Kobayashi-Maskawa (CKM) picture — four quark-mixing parameters, with a single CP-violating phase — jointly accounts for the competitive measurements of kaon mixing, $B^0$--$��bar B^0$ mixing, semileptonic decay rates, and the CP asymmetries $��sin 2��beta$ and $��sin 2��alpha$. It performs a global fit to those inputs and reports a toy-Monte-Carlo probability of 71% that the Standard Model could produce data at least as discrepant as the observed set, with $��chi^2_{��min;y_{��rm mod}}=0.6$ (Eqs. 73–74). If that reading holds, the KM phase is the dominant source of CP violation at the electroweak scale, and the fit's one- and two-dimensional ranges become reference targets for interpreting the next round of B and kaon measurements. The paper also tests whether penguin-dominated observables or a model-independent parameterization of gluonic-penguin new physics require departures from that picture; it finds none that are unambiguous, though it notes evidence for potentially large rescattering effects.

What carries the argument

The load-bearing device is the Rfit frequentist scheme: a likelihood in which experimental measurements contribute a $��chi^2$, while each poorly known QCD parameter is allowed to vary freely inside a pre-assigned range and costs nothing in $��chi^2$ while inside it (Part II, Eq. 31). That scheme turns the unitarity-triangle apex $(��bar��rho,��bar��eta)$ into the two-parameter space in which confidence levels are drawn, with all other CKM and hadronic parameters minimized away. The extraction of $��sin 2��alpha$ from $B��to��rho��rho$ uses the isospin relations among the three charge states, extended to include electroweak penguins; the QCD-factorization comparison uses calculated $��pi��pi$ and $K��pi$ amplitudes; and the new-physics section replaces the SM penguin amplitudes with a model-independent parameterization of $b��to d$ and $b��to s$ gluonic contributions.

Extended reading notes

Core claim

The central claim is that the standard CKM fit, built from $|V_{us}|$, $|V_{ud}|$, $|V_{ub}|$, $|V_{cb}|$, $|��varepsilon_K|$, $��Delta m_d$, $��Delta m_s$, $��sin 2��beta[c��bar c s]$ and $��sin 2��alpha[��rho��rho]$, is internally consistent: the fit returns $��chi^2_{��min;y_{��rm mod}}=0.6$ and a 71% p-value for the Standard Model hypothesis (Section III.3.1, Eqs. 73–74). On that basis the paper extracts allowed ranges for the Wolfenstein parameters, the CKM elements and many derived observables (Tables 2 and 3), and proposes including $��sin 2��alpha$ from $B^0��to��rho^+��rho^-$ through isospin relations that separate the penguin contribution. It further reports that a QCD-factorization fit to the $��pi��pi$ and $K��pi$ data agrees with the other unitarity-triangle constraints and yields predictions for related observables, while the $B��to K��pi$ data are not precise enough to constrain electroweak or hadronic parameters. The new-physics analysis in $b��to d$ and $b��to s$ gluonic penguins finds that significant non-standard corrections cannot be excluded, but standard solutions are favored in most cases.

Load-bearing premise

The fit's consistency figure and all quoted ranges are valid only if every nonperturbative QCD parameter — $f_{B_d}��sqrt{B_d}$, $B_K$, $��xi$, and the rest — lies inside its pre-assigned allowed range and can be varied freely within that range without cost.

Editorial extensions

If this is right

The four Wolfenstein parameters and the derived CKM elements in Tables 2 and 3 provide a common reference against which later B-factory and kaon measurements can be judged.
Including $��sin 2��alpha[��rho��rho]$ modestly improves the knowledge of $��alpha$ and $��gamma$; a future measurement of $B^0��to��rho^0��rho^0$ branching fraction and CP asymmetries would remove discrete ambiguities in the isospin analysis.
A QCD-factorization fit to all $��pi��pi$ and $K��pi$ data yields predictions for the related observables, while the data themselves prefer sizable phenomenological power corrections.
The model-independent gluonic-penguin analysis leaves room for non-standard corrections, but the standard solution is favored in most cases, so a new-physics interpretation of penguin CP asymmetries remains possible but not required.
A future $K^+��to��pi^+��nu��bar��nu$ measurement near 10% precision, combined with improved $|V_{cb}|$, $m_t$ and $m_c$, would turn the rare-kaon mode into a competitive constraint on $|V_{td}|$; a $K_L��to��pi^0��nu��bar��nu$ observation would constrain $|��eta|$.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The 71% p-value is a statement about the whole fit conditional on the allowed-range choices, not a proof that the CKM picture is unique; a reader should treat the quoted 5% contours as conservative frequentist envelopes rather than posterior credible regions.
If the fit holds, the most informative place to look for new physics is not the magnitudes of CKM elements but the CP-violating phases and rescattering phases in penguin-dominated modes, where the Standard Model allowance is largest.
The $��rho��rho$ isospin constraint will become decisive once $B^0��to��rho^0��rho^0$ is measured; until then the modest improvement in $��alpha$ should not be read as a precision determination.
Because the rare-kaon predictions depend on the same CKM inputs but different hadronic inputs, a future branching fraction outside the fit's predicted range would be a cleaner discrepancy than a shift in a single B observable.

Original abstract

We update the profile of the CKM matrix. The apex (rhobar,etabar) of the Unitarity Triangle is given by means of a global fit. We propose to include therein sin2alpha from the CP-violating asymmetries in B0->rho+rho-, using isospin to discriminate the penguin contribution. The constraint from epsilon'/epsilon is briefly discussed. We study the impact from the measurement of the rare decay K+->pi+nunu-bar, and from a future observation of KL->pi0nunubar. The B system is investigated in detail, beginning with 2beta+gamma and gamma from B0->D(*)+-pi-+ and B+->D(*)0K+. A significant part of this paper is dedicated to B decays into pipi, Kpi, rhopi and rhorho. Various phenomenological and theoretical approaches are studied. Within QCD Factorization we find a remarkable agreement of the pipi and Kpi data with the other UT constraints. A fit of QCD FA to all pipi and Kpi data leads to precise predictions of the related observables. We analyze separately the B->Kpi decays, and in particular the impact of electroweak penguins in response to recent phenomenological discussions. We find no significant constraint on electroweak nor hadronic parameters. We do not observe any unambiguous sign of New Physics, whereas there is some evidence for potentially large rescattering effects. Finally we use a model-independent description of a large class of New Physics effects in both BBbar mixing and B decays, namely in the b->d and b->s gluonic penguin amplitudes, to perform a new numerical analysis. Significant non-standard corrections cannot be excluded yet, however standard solutions are favored in most cases.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.89 · human participants 0.01 · controlled comparison 0.08 · randomized assignment 0.01 · states quantitative result 0.11 · compares with prior results 0.63 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; show every role.

We update the profile of the CKM matrix. The apex (rhobar,etabar) of the Unitarity Triangle is given by means of a global fit. We propose to include therein sin2alpha from the CP-violating asymmetries in B0->rho+rho-, using isospin to discriminate the penguin contribution. The constraint from epsilon'/epsilon is briefly discussed. We study the impact from the measurement of the rare decay K+->pi+nunu-bar, and from a future observation of KL->pi0nunubar. The B system is investigated in detail, beginning with 2beta+gamma and gamma from B0->D(*)+-pi-+ and B+->D(*)0K+. A significant part of this paper is dedicated to B decays into pipi, Kpi, rhopi and rhorho. Various phenomenological and theoretical approaches are studied. Within QCD Factorization we find a remarkable agreement of the pipi and Kpi data with the other UT constraints. A fit of QCD FA to all pipi and Kpi data leads to precise predictions of the related observables. We analyze separately the B->Kpi decays, and in particular the impact of electroweak penguins in response to recent phenomenological discussions. We find no significant constraint on electroweak nor hadronic parameters. We do not observe any unambiguous sign of New Physics, whereas there is some evidence for potentially large rescattering effects. Finally we use a model-independent description of a large class of New Physics effects in both BBbar mixing and B decays, namely in the b->d and b->s gluonic penguin amplitudes, to perform a new numerical analysis. Significant non-standard corrections cannot be excluded yet, however standard solutions are favored in most cases.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We update the profile of the CKM matrix.	contribution 0.99	0.89	0.04	asserted 0.89
s1	The apex (rhobar,etabar) of the Unitarity Triangle is given by means of a global fit.	result 0.40	0.83	0.05	asserted 0.99
s2	We propose to include therein sin2alpha from the CP-violating asymmetries in B0->rho+rho-, using isospin to discriminate the penguin contribution.	contribution 0.63	0.68	0.05	asserted 0.32
s3	The constraint from epsilon'/epsilon is briefly discussed.	contribution 0.93	0.48	0.02	asserted 0.56
s4	We study the impact from the measurement of the rare decay K+->pi+nunu-bar, and from a future observation of KL->pi0nunubar.	contribution 0.98	0.61	0.04	asserted 0.73
s5	The B system is investigated in detail, beginning with 2beta+gamma and gamma from B0->D()+-pi-+ and B+->D()0K+.	contribution 0.98	0.74	0.03	asserted 0.97
s6	A significant part of this paper is dedicated to B decays into pipi, Kpi, rhopi and rhorho.	contribution 0.99	0.60	0.03	asserted 1.00
s7	Various phenomenological and theoretical approaches are studied.	contribution 0.55	0.59	0.02	asserted 0.91
s8	Within QCD Factorization we find a remarkable agreement of the pipi and Kpi data with the other UT constraints.	result 1.00	0.93	0.13	asserted 1.00
s9	A fit of QCD FA to all pipi and Kpi data leads to precise predictions of the related observables.	result 0.88	0.91	0.10	asserted 1.00
s10	We analyze separately the B->Kpi decays, and in particular the impact of electroweak penguins in response to recent phenomenological discussions.	contribution 0.97	0.76	0.04	asserted 0.75
s11	We find no significant constraint on electroweak nor hadronic parameters.	result 0.99	0.95	0.13	asserted 0.99
s12	We do not observe any unambiguous sign of New Physics, whereas there is some evidence for potentially large rescattering effects.	result 0.60	0.94	0.28	asserted 0.58
s13	Finally we use a model-independent description of a large class of New Physics effects in both BBbar mixing and B decays, namely in the b->d and b->s gluonic penguin amplitudes, to perform a new numerical analysis.	contribution 0.77	0.93	0.08	asserted 0.98
s14	Significant non-standard corrections cannot be excluded yet, however standard solutions are favored in most cases.	interpretation 0.52	0.81	0.38	hedged possibility 0.81

What kind of paper the classifier reports this is: theoretical result 0.45 · evidence from analysis of existing data 0.98.

What was examined, and what was not

sources read

arXiv listing abstract v3

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures

**Figure 1.** The rescaled Unitarity Triangle in the Wolfenstein parameterization. and, using the Wolfenstein parameterization, one finds J = A 2λ 6 η 1 − λ 2 /2 + O(λ 10) ∼ 10−5 . (11) The empirical value of J is small compared to its mathematical maximum of 1/(6√ 3) ≃ 0.1 showing that CP violation is suppressed as a consequence of the strong hierarchy exhibited by the CKM matrix elements. Remarkably, to account for CP violation (see Eq. (8)) requires not only a non-zero J but also a non-degenerated quark-mass hierarchy. Equal masses for at least two generations of up-type or down-type…

**Figure 2.** Constraints in the unitarity plane for the most relevant observables. The theoretical parameters used correspond to some “standard” set chosen to reproduce compatibility between the observables. exhibiting small CP asymmetries. The UT (12) is sketched in

**Figure 3.** Difference between Eq. (37) and a Monte Carlo evaluation of the confidence level for various measurements of a hypothetical quantity sin(x). The Monte Carlo evaluation takes into account the physical boundaries of the observable. 7. the CL referring to the coordinate a0 is then given by P(a0) ≤ Z ∆χ2≥∆χ2(a0) Fa0 (∆χ 2 ) d∆χ 2 . (43) An illustration of the difference between a straight application of Eq. (37) and the accurate Monte Carlo result is given for various measurements of a hypothetical quantity sin(x) in

**Figure 4.** Left: Hat functions (x0 = 0 and σo = 1) used for the Rfit scheme, the ERfit scheme, and the Gaussian treatment. Right: combined likelihood expLsyst (with x0 = 0 and σexp = σo = 1) for the Rfit scheme, the ERfit scheme, a convolution of a Gaussian with a uniform distribution (hence taken as a PDF, following the Bayesian approach) and a convolution of two Gaussians. more can be said in generality. For experimental and theoretical systematics where x0 can be assumed to be an unknown offset14: the quantity to be confronted to the theoretical prediction xtheo is simply xexp + x0.…

**Figure 5.** Simulated F(χ 2 ) distribution and corresponding SL curve for the standard CKM fit. The arrow indicates the corresponding minimal χ 2 min;ymod found in the analysis. for the validity of the SM. One notices that compared to previous fits [ 6], the “unitarity problem” in the first row, that is the incompatibility between |Vud| and 1−|Vus| 2 , becomes insignificant with the likelihoods we use for these two quantities (see the discussion in Section 2.1 and subsequent paragraphs). Their average has χ 2 min;|Vud|,|Vus| = 0.16. The large p-value of the electroweak sector of the SM when…

**Figure 6.** Confidence levels in the enlarged (ρ, η) plane for the global CKM fit. The shaded areas indicate the regions of ≥ 5% CLs. For sin 2β the ≥ 32% and ≥ 5% CL constraints are shown. The upper (lower) plot excludes (includes) the constraints from sin 2β and sin 2α in the combined fit. The hatched area in the center of the combined fit result indicates the region where theoretical errors dominate. The lower plot corresponds to the standard CKM fit

**Figure 7.** Confidence levels in the (ρ, η) plane for the global CKM fit. The shaded areas indicate the regions of ≥ 5% CLs. For sin 2β the ≥ 32% and ≥ 5% CL constraints are shown. The upper (lower) plot excludes (includes) the constraints from sin 2β and sin 2α in the combined fit. The hatched area in the center of the combined fit result indicates the region where theoretical errors dominate. The lower plot corresponds to the standard CKM fit. decays26 as well as a selection of theoretical parameters. In the case of such one-dimensional displays, the a parameter is defined by the x…

**Figure 8.** Confidence levels for the Wolfenstein parameters and UT surface and angles obtained from the standard CKM fit (shaded areas). The dotted curves give the results without using sin 2β and sin 2α[ρρ] in the fit, while the dashed line excludes only sin 2α[ρρ] . 6.8 × 10−6 [ 154]. While the µ +ν limit is still an order of magnitude larger than the expected value, the experiments approach the sensitivity required for a discovery of B+ → τ +ν. It may become one of the key analyses in the coming years. 3.4 Is there a sin 2β Problem in Penguin-Dominated Decays? As pointed out in Section II

**Figure 9.** Confidence levels for the various sin 2β[eff] measurements that are believed to be dominated by a single CKM phase, their averages and the result from the standard CKM fit

**Figure 10.** Allowed values for the hadronic parameters R6 and R8, using the experimental average of Re(ε ′/ε) and the result on Im(VtdV ∗ ts) from the standard CKM fit as input. The symbols with error bars give the theoretical predictions taken from Refs. [ 164, 172, 173, 174, 175]. where ΩIB = 0.06 ± 0.08 corrects for isospin-breaking [ 172], Λ (4) MS = (340 ± 30) MeV is the characteristic QCD scale for 4 active quark flavors in the MS scheme, and where R6 and R8 are defined by R6 = B (1/2) 6 121 MeV ms(mc) 2 , R8 = B (3/2) 8 121 MeV ms(mc) 2 , (78) with the running s-qua

**Figure 11.** Confidence level of B(K+ → π +νν) (left) and |Vtd| (right). The solid lines give to the constraints from the combined E787 and E949 measurements, and the hatched areas represent the SM predictions obtained from the standard CKM fit. with X(x) = ηXX0(x) , σ = 1 + λ 2 + O(λ 4 ) , ρ0 = 1 + P0 A2X(xt) . (82) Equation (79) provides an almost elliptic constraint in the (ρ, η) with the center close to the (ρ = 1, η = 0) apex of the Unitarity Triangle. It allows us to extract the CKM matrix element |Vtd| from the branching fraction measurement. The constant κ+ is defined in Ref. [ 180]. It…

**Figure 12.** Constraint in the (ρ, η) plane from the combined E787 and E949 measurements of B(K+ → π +νν) (left), and from a hypothetical B(K0 L → π 0νν) measurement with 10% relative error (right). Dark, medium and light shaded areas have CL > 0.90, 0.32 and 0.05, respectively. (I) using the present knowledge of the relevant input parameters and neglecting the statistical error on the B(K+ → π +νν) measurement; (II) assuming a measurement with a statistical precision of 10% and an improvement of the relevant uncertainties to a 1% error on |Vcb|, a 2 GeV error on the top quark mass, and a 50 Me

**Figure 13.** Constraint in the enlarged (ρ, η) plane from the average measurement of timedependent CP-violating asymmetries in B0 → D∗±π ∓ decays. The shaded areas indicate CL > 5% (light), CL > 32% (medium) and CL > 90% (dark) regions. Also shown is the CL > 5% region of the standard CKM fit. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Average (toy MC) Average (χ 2 ) CKM fit BABAR | sin(2β+γ) | CL D ( * )+– π –+ CK M f i t t e r Winter 2004 0 0.2 0.4 0.6 0.8 1 1.2 1.4 -150 -100 -50 0 50 100 150 Combined | sin(2β+γ) | and sin(2β) CKM fit γ (deg) CL D ( * )+– π –+ CK M f…

**Figure 14.** Left: confidence level obtained for |sin(2β + γ)|. The shaded area gives the average from BABAR and Belle obtained by means of a toy Monte Carlo simulation (see Section II.2.2.3). As a comparison, we show by the solid line the approximate result from the Prob(χ 2 , 1) interpretation. Also shown is the result from BABAR only, which leads to a stronger exclusion of small |sin(2β + γ)| values due to the somewhat propitiously small value of c ∗ in partially reconstructed B0 → D∗±π ∓ decays [ 187]. Also shown is the prediction from the standard CKM fit. Right: confidence level obtained

**Figure 15.** Confidence levels obtained for the strong phases δ (∗) occurring between the CKMfavored and CKM-suppressed branches of B0 → D∗±π ∓ decays. The standard CKM fit has been used to constrain the weak CKM phases. B0 → D(∗)±π ∓ measurements to constrain the strong phases δ (∗) as shown in

**Figure 16.** Confidence level of the UT angle γ from the Dalitz plot analysis of B+ → D(∗)0K+ decays [ 195, 196]. Shown are the experimental PDF (solid line - statistical only), found by Belle, and the corresponding CL from single-sided integration (shaded area - including systematics, while the dashed line gives the CL obtained when ignoring systematic uncertainties). Also given is the constraint from the standard CKM fit. -1.5 -1 -0.5 0 0.5 1 1.5 -1 -0.5 0 0.5 1 1.5 2 α βγ Standard CKM Fit ρ η shaded areas have CL > 0.05, 0.32, 0.90 D ( * )0K C K M + f i t t e r Winter 2004 CL=0.05…

**Figure 17.** Confidence level in the enlarged (ρ, η) plane from the Dalitz plot analysis of B+ → D(∗)0K+ decays [ 195, 196]. The shaded areas indicate CL > 5% (light), CL > 32% (medium) and CL > 90% (dark) regions. The hatched area indicates the CL > 5% region when ignoring systematic uncertainties. Also shown is the CL > 5% constraint from the standard CKM fit

**Figure 18.** Example of tree (left) and penguin (right) diagrams for the decay B0 → π +π −. for which the u (U), c (C) and t (T) amplitude coefficients have been substituted respectively. In the following, we adopt convention C so that A+− reads A +− = VudV ∗ ubT +− + VtdV ∗ tbP +− , (95) where T +− and P +− are defined by T +− ≡ Mu − Mc and P +− ≡ Mt − Mc . (96) The particular choice of which amplitude to remove in the definition of a total transition amplitude is arbitrary34 and does not have observable physical implications. However the convention does modify the contents of the ph

**Figure 19.** Color-suppressed tree diagram for the decay B0 → π 0π 0 . where the phase arg[q/p] = 2 arg[VtdV ∗ tb] ≈ −2β (in our phase convention) arises due to B0B0 mixing. We have used in the above equations that π +π − is a CP eigenstate with eigenvalue +1. In the absence of penguin contributions (P = 0), Eq. (99) reduces to λππ = e 2iα (using the triangle definition (20)) and hence S +− ππ [P +− = 0] = sin 2α and C +− ππ [P +− = 0] = 0 . (100) In general, the phase of λππ is modified by the interference between the penguin and the tree amplitudes. In addition, the parameter C +−

**Figure 20.** The isospin relations (107) in the complex plane neglecting electroweak penguins. Note that the relative B0B0 mixing phase is included in the B triangle (A˜ij ≡ e −2iβA ij ). Using convention C, one can write √ 2A +0 ≡ √ 2A(B + → π +π 0 ) = VudV ∗ ubT +0 + VtdV ∗ tbP EW , √ 2A 00 ≡ √ 2A(B 0 → π 0π 0 ) = VudV ∗ ubT 00 C + VtdV ∗ tbP 00 , (106) and similarly for the CP-conjugated modes. The C subscript stands for the color-suppressed amplitude (see

**Figure 21.** Left: penguin diagram for the decay B0 → K+π −. Right: OZI-suppressed penguin annihilation diagram for the decay B0 → π +π −. 1.2.2 SU(3) Flavor Symmetry We extend the use of flavor symmetries to SU(3), considering the amplitude of the decay B0 → K+π − in convention C A +− Kπ ≡ A(B 0 → K+π −) = VusV ∗ ubT +− Kπ + VtsV ∗ tbP +− Kπ . (122) With the assumption of SU(3) flavor symmetry and neglecting OZI-suppressed penguin annihilation diagrams (see right hand diagram in

**Figure 22.** W exchange diagram responsible for the decay B0 → K+K−. power corrections is quite successful within large theoretical uncertainties, but it can no longer be viewed as a systematic expansion of QCD. 1.3 Experimental Input The experimental values for the time-dependent CP asymmetries measured by BABAR [ 219] and Belle [ 220] are collected in

**Figure 23.** Confidence levels for α for Scenarios (I) through (IV) (cf. Section VI.1.2) of the B → ππ data. The dark shaded function on the upper left hand plot shows the constraint from SU(2) when the experimental uncertainty on S +− ππ is set to zero. It hence displays the uncertainty on |α − αeff| due to the penguin contribution. Also shown on each plot is the result from the standard CKM fit. 1.4.1 Constraints on α and (ρ, η) The constraints on α and in the (ρ, η) plane obtained for the various scenarios are plotted in Figs. 23 and 24 and discussed below41 . • At present, we achieve…

**Figure 24.** Confidence levels in the (ρ, η) plane for Scenarios (I) through (IV) of the B → ππ data. Dark, medium and light shaded areas have CL > 0.90, 0.32 and 0.05, respectively. Also shown on each plot is the result from the standard CKM fit. Significant constraints are obtained once the penguin-to-tree ratio is determined with the use of phenomenological or theoretical input (Scenarios (III) and (IV)). Consistency with the SM is found, in spite of the sensitivity of the data to b → d transitions that could in principle receive sizable New Physics contributions

**Figure 25.** Predictions for S +− ππ and C +− ππ for Scenarios (I) through (IV). Drawn are CL = 0.05 contours. The input values for ρ and η are taken from the standard CKM fit assuming the SM to hold. The dot with error bars gives the QCD FA prediction obtained from the global fit to all B → ππ, Kπ observables (excluding S +− ππ or C +− ππ from the fit when determining C +− ππ and S +− ππ , respectively) presented in Section II.2.3. For comparison, the CL contours corresponding to 1σ and 2σ for the experimental results from BABAR, Belle and their averages are overlaid. Note that we have applied…

**Figure 26.** Constraints on the penguin-to-tree ratio r +− and the relative strong phase δ +− in B → ππ decays, obtained when using as additional input the CKM parameters ρ and η from the standard CKM fit. The gradually shaded regions give the CLs for fits of Scenario (I) (SU(2)): dark, medium and light shaded areas have CL > 0.90, 0.32 and 0.05, respectively. Also shown are the 5% CL contours obtained for Scenario (II) and (III). The elliptical areas are the prediction from QCD Factorization (Scenario (IV)): full calculation (light shaded) and leading order (dark shaded). On the right hand…

**Figure 27.** Constraints from Scenario (I) (SU(2)) on magnitude and phase of the colorsuppressed-to-color-allowed ratio T 00 C /T +− in B → ππ decays. The CKM parameters ρ and η are taken from the standard CKM fit. The gradually shaded regions indicate the CLs: dark, medium and light shaded areas have CL > 0.90, 0.32 and 0.05, respectively. C 00 ππ = 0.13, and with all other parameters kept unchanged). The quality of the metrological constraint on α depends on how much the different solutions overlap. The worst case occurs when several mirror solutions gather around the true value of α within…

**Figure 28.** Left: confidence level as a function of α for the full isospin analysis (including C 00 ππ) at an integrated luminosity of 1 ab−1 , and using the central values and errors given in the text (shaded area). Also shown is the CL for B 00 ππ = 1.2×10−6 (down-diagonal hatched area) for which the ambiguities move together (see right hand plot), and for B 00 ππ = 0.66 × 10−6 (up-diagonal hatched area), which corresponds to B 00 GLSS− , i.e., the ambiguities overlap in two quadruplets. The branching ratio values given on the figure are in units of ×10−6 . Right: location of the eight…

**Figure 29.** Confidence level in the (α,C00 ππ) plane at integrated luminosities of 1 ab−1 (left) and 10 ab−1 (right), respectively. The observable set and errors used are given in the text. -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 0 0.05 0.1 0.15 0.2 0.25 x 10 -5 shaded areas have CL > 0.05, 0.32 ρ,η CKM fit B 00 C00 C K M f i t t e r Winter 2004 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 0 0.05 0.1 0.15 0.2 0.25 x 10 -5 shaded areas have CL > 0.05, 0.32 ρ,η perfect B 00 C00 C K M f i t t e r Winter 2004

**Figure 30.** Confidence level in the (B 00 ππ,C00 ππ) plane at an integrated luminosity of 1 ab−1 . The left hand plot uses the standard CKM fit as input including the present uncertainties on α, while the right hand plot assumes perfect knowledge of α. Superimposed on the left hand plot is the analytical function C 00 ππ(B 00 ππ) (119), where electroweak penguins are neglected which explains the difference with the CL function. The vertical line represents the bound (117). C s KK B s KK τB0 s + C +− ππ B +− ππ τB0 = 0 , (131) where C s KK = C(B0 s → K+K−) and B s KK denote the direct…

**Figure 31.** Confidence level in the (B s KK, −C s KK) plane obtained from B → ππ data and the standard CKM fit, assuming SU(3) symmetry. Also shown is the preliminary result on the ratio B(B0 s → K+K−)/B(B0 → K+π −) from CDF [ 224, 231] and the branching fraction (corrected by the lifetime ratio τB0 s /τB0 ) and direct CP asymmetry in B → K+π −. The bands indicate 1σ error ranges. These predictions can be compared with the branching fraction and CP asymmetry found for B0 → K+π − (see

**Figure 32.** Confidence levels in the (ρ, η) plane for the QCD FA at leading order using S +− ππ and C +− ππ from BABAR (upper left), Belle (upper right) and their averages (bottom). Left: dark, medium and light shaded areas have CL > 0.90, 0.32 and 0.05, respectively. Right: the maximum CL is set to 10−3 : dark, medium and light shaded areas have CL > 90 × 10−5 , 32 × 10−5 and 5 × 10−5 . Also shown on each plot is the result from the standard CKM fit

**Figure 33.** Confidence level in the (ρ, η) plane for Scenario (IV): using branching fractions and CP-violating asymmetries of B → ππ decays (upper left hand plot), B → Kπ decays (upper right hand plot) and all together (lower plot). Dark, medium and light shaded areas have CL > 0.90, 0.32 and 0.05, respectively. Also shown is the constraint from the standard CKM fit

**Figure 34.** Distributions of χ 2 min from toy Monte Carlo experiments and corresponding significance level curves for full QCD FA fits to combined B → ππ and B → Kπ results (solid line). BABAR and Belle averages are used for S +− ππ and C +− ππ . The dashed lines give the results for unbound parameters ρA and ρH (see text for details). The constraints in the (ρ, η) plane using the LO prediction are shown in

**Figure 35.** Comparison of the results from the global QCD FA fit to B → ππ, Kπ data (shaded boxes) and the unconstrained QCD FA predictions with experiment for the CP-violating asymmetries (left) and the branching fractions (right) in B → hh′ (h,h′ = π,K) decays. The predictions are obtained ignoring the measurement associated with the observable in the fit. The experimental results are the world averages quoted in

**Figure 36.** Confidence level in the (B(K0π 0 ),B(K+π −)) plane obtained from the global QCD FA fit to B → ππ, Kπ data ignoring the measurements associated with the observables shown. Dark, medium and light shaded areas have CL > 0.90, 0.32 and 0.05, respectively. The hatched areas indicate the 1σ error bands of the experimental results

**Figure 37.** Left: confidence level as a function of the CKM angle α, in the Nir–Quinn approximation (no electroweak penguins). The hatched region represents the constraint from the standard CKM fit. Right: constraint on the annihilation-to-tree amplitude ratio |N0+/T +−|, as defined in Eq. (147). Electroweak penguins are neglected. Note that Eqs. (144) and (145) separately hold for the T ij and P ij . Under these assumptions it is possible to describe the full B → Kπ system with four out of the seven complex quantities T ij and P ij . In the following parameterization, we use P +− and the…

**Figure 38.** Confidence level in the (ρ, η) plane for the isospin analysis of B → Kπ decays within the framework of Ref. [ 243] (see text). In the left hand plot N0+ is set to zero, while in the right hand plot it is allowed to vary freely within 10% of the T +− dominant amplitude. Dark, medium and light shaded areas have CL > 0.90, 0.32 and 0.05, respectively. Also shown on each plot is the prediction from the standard CKM fit. 3.3.2 Standard Model Electroweak Penguins and Vanishing Annihilation Topologies Since the pioneering work of Nir and Quinn it has been realized that gluonic penguins…

**Figure 39.** Constraints on the complex tree-to-penguin amplitude ratio in B0 → K+π − decays (left), and the complex color-suppressed-to-color-allowed amplitude ratio (right), obtained when using as additional input the CKM parameters ρ and η from the standard CKM fit. The gradually shaded regions give the CLs within the framework of Ref. [ 243]: dark, medium and light shaded areas have CL > 0.90, 0.32 and 0.05, respectively. determined, up to discrete ambiguities (see also Ref. [ 245] for a short review of other approaches analyzing the Kπ system). The additional hypotheses are • negligible…

**Figure 40.** Constraints on the complex quantities XEW (left, where XEW C is fixed to 1) and XEW C (right, where XEW is fixed to 1) defined in Eq. (154) and (155), respectively. Dark, medium and light shaded areas have CL > 0.90, 0.32 and 0.05, respectively. The standard CKM fit is used as input to obtain these plots. where we have imposed R+ = R− ≡ R. Within the SM and under the assumptions already explicitly stated, we expect XEW ≈ XEW C ≈ 1. We introduce two new fit scenarios: a first where XEW ≡ 1 and XEW C is free to vary in the fit (magnitude and phase), and a second where conversely XEW…

**Figure 41.** Ratios of branching fractions (156) versus the direct CP asymmetry parameter in B+ → K+π 0 decays as predicted from B → ππ and the standard CKM fit, assuming SU(3) flavor symmetry and neglecting all annihilation and exchange diagrams. Dark, medium and light shaded areas have CL > 0.90, 0.32 and 0.05, respectively. The hatched bands indicate the 1σ regions of the corresponding measurements. (See also

**Figure 42.** Confidence level in the A+− ρπ versus A−+ ρπ (left plot) and B +− ρπ versus B −+ ρπ (right plot) planes. Shown are the 1σ (dark shaded), 2σ (medium shaded) and the 3σ (light shaded) regions. The dashed line in the right hand plot approximately indicates vanishing dilution (∆Cρπ = 0, neglecting AρπCρπ 6= 0). and the correlation coefficients Bρ−π+ Bρ+π− Bρ−π+ Bρ+π− −0.17 −0.47 −0.14 Bρ−π+ 1 −0.08 −0.40 Bρ+π− − 1 −0.06 (175) One notices a significant lack of B0 → ρ +π − decays in the results (174). We can infer from these numbers the B-flavor-averaged branching fractions (in units of…

**Figure 43.** Constraint on the UT angle α using the CP and branching fraction results for B0 → ρ ±π ∓ decays and assuming vanishing penguin contributions. Indicated by the dark-shaded areas are the solutions when further fixing the relative strong phase ˆδ to zero. Also shown is the constraint from the standard CKM fit. 4.3 Penguins The experimental results on K∗π and Kρ modes summarized in

**Figure 44.** Confidence levels in the complex planes |Rt/Ru|(P +−/T +−) (left) and |Rt/Ru|(P −+/T −+) (right), using α from the standard CKM fit as input. Dark, medium and light shaded areas have CL > 0.90, 0.32 and 0.05, respectively. Shown by the hatched areas are the corresponding CL > 0.05 regions obtained when using in addition SU(3) flavor symmetry (Scenario (II), see Section 4.5). larger direct CPV, more sizable penguin-to-tree ratios are required here. The characteristic hyperbolic shapes of the constraints is due to the fact that direct CP violation is the product of penguin-to-tree…

**Figure 45.** Left: constraint on α using the full B → ρπ isospin analysis and assuming projections into future integrated luminosities of 1 ab−1 and 10 ab−1 . The assumptions made on the generating amplitudes are given in the text. The arrow indicates the true value of α used for the generation of the toy observables. The hatched area shows the constraint obtained from the present standard CKM fit. Right: same as left hand plot but with a ten times smaller B 00 ρπ. results given in

**Figure 46.** Left: Confidence levels for the SU(3) bounds (185) (dashed line) and (186) (solid line). The arrows indicate the CL = 0.05 crossing values given in Eq. (187). Right: Lower bounds on the branching fractions B +− K∗π (dashed line) and B −+ ρK (solid line) obtained with the use of SU(3) symmetry and inserting α from the standard CKM fit. The arrows indicate the corresponding experimental values (same line types). 4.5 SU(3) Flavor Symmetry Similarly to the studies in B0 → hh′ decays, one can use SU(3) flavor symmetry and dynamical hypotheses to obtain additional information on the…

**Figure 47.** The direct CP-violating asymmetries A+− ρπ versus A−+ ρπ bound using SU(3) flavor symmetry and the measured flavor-specific branching ratios (176) as the only input. Dark, medium and light shaded areas have CL > 0.90, 0.32 and 0.05, respectively. Also shown are the experimental values found by BABAR. 4.5.2 Estimating |P +−| and |P −+| from B+ → ρ +K0 and B+ → K∗0π + The magnitude of the penguin amplitudes |P +−| and |P −+| can be estimated from the branching fraction of the penguin-dominated decays B+ → ρ +K0 and B+ → K∗0π + (Scenario (III)). Neglecting the doubly CKM-suppressed u…

**Figure 48.** Left: confidence levels obtained for α with the use of SU(3) flavor symmetry within Scenario (II). The light shaded curve gives the nominal constraint, while the dark shaded one corresponds to the solutions one would obtain if the relative strong phase ˆδ were known and equal to zero. The hatched area shows the constraint obtained from the CKM fit using the standard constraints (cf. Part III). Right: correlation between α and ˆδ. The shaded areas indicate CL = 0.32 domains and the solid lines show the CL = 0.05 regions. The periodicity is ∆α = 45◦ and ∆ˆδ = 90◦ . The hatched area…

**Figure 49.** Confidence levels obtained for α with the use of SU(3) flavor symmetry. Left: Scenario (II) (light shaded, same as in left hand plot of

**Figure 50.** Confidence levels for α from the SU(2) analysis of the B → ρρ system (light shaded). The dark-shaded function is obtained by setting the error on S +− ρρ,L to zero. It hence represents the uncertainty due to the penguin contribution (∆α). Also shown is the prediction from the standard CKM fit (hatched area), which includes the world average for sin 2β but ignores the B → ρρ data. 5.1 Theoretical Framework and Experimental Input Due to the lack of experimental information, an SU(3) analysis is not feasible at present (the branching fractions of the SU(3) partners B0 → K∗+ρ − and the…

**Figure 51.** Confidence levels from the SU(2) analysis of the B → ρρ system. Dark, medium and light shaded areas have CL > 0.90, 0.32, 0.05, respectively. Left: constraints in the (ρ, η) plane. Overlaid is the prediction from the standard CKM fit, which includes the world average for sin 2β but not the B → ρρ data. Right: constraints in the (S +− ρρ,L,C+− ρρ,L) plane, with the input values for ρ and η taken from the standard CKM fit. The circle indicates the physical limit S +− ρρ,L 2+C +− ρρ,L 2 = 1, and the hatched area represents the CL of the BABAR measurement for which the presence of the…

**Figure 52.** Constraints on the penguin-to-tree ratio (Rt/Ru)|P +−/T +−| and the relative strong phase arg[P +−T +−∗] (left), and on the color-suppressed to color-allowed ratio |T 00 C /T +−| and the relative strong phase arg[T 00 C T +−∗] (right), obtained from the SU(2) analysis and using the result from the standard CKM fit as input. Dark, light and very light shaded areas have CL > 0.90, 0.32, 0.05, respectively

**Figure 53.** Confidence levels for B(B+ → ρ +ρ 0 ) versus B(B0 → ρ +ρ −) (left) and B(B+ → ρ +ρ 0 ) versus B(B0 → ρ 0ρ 0 ) (right), obtained from the isospin analysis ignoring the branching fractions that are determined, and with the use of α from the standard CKM fit. The hatched areas indicate the 1σ bands of the corresponding measurements. at CL > 5% (2σ). The penguin error contains a systematic uncertainty of 0.2 ◦ (interpreted as a theory error by Rfit) from the treatment of the electroweak penguins (see Eq. (121) in Section VI.1.2.1). The full shift on α introduced by P EW amounts to −2.1…

**Figure 54.** Confidence level for α from the SU(2) analysis of the B → ρρ system, extrapolated at integrated luminosities of 500 fb−1 (light shaded) and 1 ab−1 (dark shaded). The two scenarios defined in the text are shown: the left (right) hand plot corresponds to a relatively large (small) value for B 00 ρρ, each one compatible with a subset of the current measurements. To illustrate the impact of the S 00 ππ measurement, we also show the result at 500 fb−1 ignoring the latter input (hatched). resolve the discrete ambiguities when relying on C 00 ρρ,L only. The main additional information on…

**Figure 55.** Confidence levels for α from the B → ρρ isospin analysis where isospin-breaking corrections (with the exception of electroweak penguins) are neglected (solid lines), and when including a relative 4% correction with arbitrary phases on the amplitude level (dashed lines), according to Eq. (192). The left hand plot gives the results for the present experimental situation (bound on B(B0 → ρ 0ρ 0 )), while the right hand plot uses the extrapolation to 1 ab−1 , defined in Section 5.3. It includes the full isospin analysis with available measurements of S 00 ρρ,L and C 00 ρρ,L. An impo

**Figure 56.** Confidence level from the SU(2) analysis of B → ππ (light shaded) and B → ρρ (dark shaded) decays as a function of α. Also shown is the prediction from the standard CKM fit (hatched area), which includes the world average of sin 2β but excludes B → ρρ. from a Dalitz plot analysis together with the SU(3) constraints from penguin-dominated partners. We conclude from the SU(2) analysis of the ρρ system that • even without a significant measurement of B(B → ρ 0ρ 0 ) a useful constraint on α is obtained. The smallness of the theoretical uncertainties allows us to include the…

**Figure 57.** Constraints in the (ρ, η) (top) and (γ, 2β + 2θd) (bottom) planes from the fit in the framework of New Physics in B0B0 mixing. The top right and bottom plots give the corresponding constraint when using only the two solutions β + θd and π + β + θd that are favored by the cos(2β + 2θd) > 0 evidence in B0 → J/ψK∗ decays (Section III.3.5)

**Figure 58.** Confidence level in the (2θd,r2 d ) plane obtained as a result of the global CKM fit that includes New Physics in B0B0 mixing. sumption that NP is negligible in the decay, any non-zero direct CP-asymmetry measurement implies η 6= 0 (e.g., the measurement of ε ′/ε > 0). Generally speaking, the solution η = 0 is not a natural value in the SM: the region of very small η corresponds to a fine-tuning scenario, in which the SM generates vanishingly small CP violation, whereas large NP couplings are needed to accommodate the data. See however Ref. [ 294] for an example of…

**Figure 59.** Confidence level in the (γ,rP ππ) plane obtained by the fit including NP in B0B0 mixing and in b → d,s transitions. can be decomposed into two independent CKM couplings70. In other words, Eq. (198) is the most general parameterization of the decay amplitude both within and beyond the SM. In the SM the ratio r P ππ is expected to be of order one: it would be equal to one if SU(3) symmetry were exact and in the limit of vanishing annihilation/exchange and electroweak penguin topologies (cf. Section VI.1.2.3). Thus, any large ( >∼ 30%) deviation would be a hint of nonstandard…

**Figure 60.** Confidence levels in the (γ,rc φK) (upper) and (γ,r u/c φK ) (lower) planes for BABAR (left) and Belle (right), obtained by the fit including NP in B0B0 mixing and in b → s transitions. On the BABAR plots, small (resp. large) values for r c φK (resp. r u/c φK ) correspond to the solution cos 2βeff < 0, and conversely. On the Belle plots, the two solutions are merged. We set CLs on the quantities r c φK and r u/c φK , where we distinguish between the BABAR and Belle results for CφK and SφK since they lead to different implications. The fit inputs used are: • the constraints on γ and…

**Figure 61.** Left: next-to-leading-order Φ 10 nlo PDF of the ∆ms measurement (solid line) and leading order PDF Φ 10 lo (dotted line), for a true value ∆ms = 10 ps−1 . The two PDFs are barely distinguishable. The leading order approximation is excellent. Right: next-to-leading-order Φ 10 nlo PDF (solid line) and Φ 11 nlo PDF, for ∆ms = 11 ps−1 (dotted line). The integral of Φ 10 nlo above ∆ms = 11 ps−1 is a good approximation of the CL of a true value ∆ms = 11 ps−1 leading to a measurement ∆ms ≤ 10 ps−1 , the latter being defined as the integral of Φ 11 0 below ∆ms = 10 ps−1

**Figure 62.** Left: next-to-leading-order Φ 17 nlo PDF of the ∆ms measurement (solid line) and leading order PDF Φ 17 lo (dotted line), for a true value ∆ms = 17 ps−1 . The two PDFs differ significantly, but the leading order approximation remains acceptable in the core of the distribution. However it would underestimate by a factor two about the probability to obtain a measurement above ∆ms = 20 ps−1 . Right: next-toleading-order Φ 17 nlo PDF (solid line) together with Φ 20 nlo PDF (dotted line) and the leading order PDF Φ 20 lo for ∆ms = 20 ps−1 (dashed-dotted line). The integral of Φ

**Figure 63.** Amplitude A solutions given in Eq. (262) (where orders up to K4 (x hyp s ) are considered in the expansion used here) for different true values of ∆ms. F(xs) = Z +∞ −∞

**Figure 64.** Likelihoods G for the T-Combiner (solid), the C-Combiner (dashed), and for the RWM method (dotted). The vertical lines indicate the locations of the two individual measurements which develop a mutual disagreement rising from the upper left figure to the lower right figure. The dotted line corresponds to the likelihood of the C-Combiner. B.4 Illustrations B.4.1 Twin Measurements To illustrate how the Combiner works, we first consider the evolution of the likelihood G as a function of the discrepancy between twin measurements xexp(1) and xexp(2), with σxexp (1) = σxexp (2) = σ0 = 1

**Figure 65.** The left plot shows the toy Monte Carlo distribution of the mean value hx[C]i as provided by the T-Combiner (shaded histogram), for a set of five consistent measurements which are Gaussian distributed around hxexpi = 5, each with a standard deviation σ(i) = 1. A Gaussian fit to the distribution results in σ = 0.47. Also shown is the weighted mean distribution (solid line) characterized by the standard deviation σWM:5 = 5−1/2 ≃ 0.45. The right hand plot shows the distribution of the RMS, σ[C], of the T-Combiner (shaded histogram) compared to the RMS, σ[RWM], of the rescaled weighted…

**Figure 66.** Likelihoods G obtained by the four approaches: T-Combiner, C-Combiner, weighted mean and the rescaled weighted mean. The vertical lines indicate the five individual measurements of which one is inconsistent. B.4.3 Inconsistent Set The second example uses the following set of N = 5 measurements: xexp(1 − 5) = 3.7, 4.2, 5.0, 5.5, 0.0, all with identical errors σxexp (1 − 5) = 1. While the first four data points are mutually compatible with a Gaussian distribution (χ 2/Ndof = 1.9/3), the last measurement is an outlier leading to a large overall χ 2/Ndof = 18.9/4, translated into a…

**Figure 67.** Distribution of the mean value hx[C]i as provided by the T-Combiner (on the vertical axis) for a set of inconsistent measurements, four of which are Gaussian distributed around hxexpi = 5, each with a standard deviation σ(i) = 1, while the fifth measurement is uniformly distributed between x5 = −5 and x5 = 15 (on the horizontal axis). The latter is effectively removed from the set by the T-Combinerwhen it departs from hxexpi by about 1.5σ(i). 0 5000 10000 2 4 6 8 〈x[C]〉 Toy experiments σ=0.56 σWM(4)=0.50 0 10000 20000 0.5 1 1.5 2 2.5 Combiner RMW σ[C]

**Figure 68.** The left plot shows the toy Monte Carlo distribution of the mean value hx[C]i as provided by the T-Combiner (shaded histogram), for a set of inconsistent measurements four of which are Gaussian distributed around hxexpi = 5, each with a standard deviation σ(i) = 1, while the fifth measurement is uniformly distributed between x5 = −5 and x5 = 15. A Gaussian fit to the distribution results in σ = 0.56, which is to be compared with the optimal WM result σWM:4 = 0.5, obtained when the fifth measurement is removed from the set. Also shown is the weighted mean distribution (solid line).…

Figures reproduced from arXiv:hep-ph/0406184 by the authors.

References

Works cited (300)

[6]

A. H¨ ocker, H. Lacker, S. Laplace and F. Le Diberder, Eur. Phys. J. C21, 225 (2001)

View on Pith 2001
[1]

N. Cabibbo, Phys. Rev. Lett. 10, 351 (1963)

View on Pith 1963
[2]

M. Kobayashi and T. Maskawa, Prog. Theor. Phys. 49, 652 (1973)

View on Pith 1973
[3]

L. Wolfenstein, Phys. Rev. Lett. 51, 1945 (1983)

View on Pith 1983
[4]

A.J. Buras, M.E. Lautenbacher and G. Ostermaier, Phys. R ev. D50, 3433 (1994)

View on Pith 1994
[5]

I.Y. Bigi, V.A. Khoze, N.G. Uraltsev and A.I. Sanda, in “CP Violation ”, C. Jarlskog Ed., World Scientiﬁc, Singapore (1988)

View on Pith 1988
[7]

Partially updated plots and results are available at the CKMﬁtter web site: http://ckmﬁtter.in2p3.fr and its mirror http://www.slac .stanford.edu/xorg/ckmﬁtter

View on Pith
[8]

M. Ciuchini, G. D’Agostini, E. Franco, V. Lubicz, G. Mart inelli, F. Parodi, P. Roudeau and A. Stocchi, J. High Energy Phys. 0107, 013 (2001)

View on Pith 2001
[9]

M. Battaglia et al. , CERN-2003-002, Cern Yellow Report, Based on the Workshop o n CKM Unitarity Triangle (CERN 2002-2003), Geneva, Switzerl and, 13-16 Feb 2002, hep- ph/0304132

View on Pith 2003
[10]

A.J. Buras, F. Parodi and A. Stocchi, J. High Energy Phys ., 0301, 029 (2003); A. Ali, Lectures given at the International Meeting on Fundamental Physics, Soto de Cangas, Spain, 23-28 Feb. 2003, hep-ph/0312303; G. Eigen, G.P. Dubo is-Felsmann, D.G. Hitlin and F.C. Porter, Contributed to International Europhysics Conference on High-Energy Physics (HEP 2003...

View on Pith Pith review arXiv 2003
[11]

L.L. Chau and W.Y. Keung, Phys. Rev. Lett. 53, 1802 (1984)

View on Pith 1984
[12]

Particle Data Group (K. Hagiwara et al.), Phys. Rev. D66, 010001 (2002 and 2003 update)

View on Pith 2002
[13]

C. Jarlskog, Phys. Rev. Lett. 55, 1039 (1985)

View on Pith 1985
[14]

G.C. Branco, L. Lavoura and J.P. Silva, CP Violation , The Intern. Series of Monographs on Physics - 103, Oxford Science Publications, Oxford, UK (1 999)

View on Pith
[15]

E787 Collaboration (S. Adler et al. ), Phys. Rev. Lett. 88, 041803 (2002)

View on Pith 2002
[16]

E949 Collaboration (A.V. Artamonov et al. ), hep-ex/0403036 (2004), http://www.phy.bnl.gov/e949

View on Pith Pith review arXiv 2004
[17]

I.S. Towner and J.C. Hardy, J. Phys. G: Nucl. Part. Phys. 29, 197 (2003)

View on Pith 2003
[18]

K. Saito and A.W. Thomas, Phys. Lett. B363, 157 (1995)

View on Pith 1995
[19]

H. Abele et al. , Phys. Rev. Lett. 88, 211801 (2002)

View on Pith 2002
[20]

D. Pocanic (for the PIBETA Collaboration), Talk given a t 2nd Workshop on the CKM Unitarity Triangle, Durham, England, 5-9 Apr 2003, eConf C0304052, WG606 References 167

View on Pith 2003
[21]

J.F. Donoghue, B.R. Holstein and S.W. Klimt, Phys. Rev. D35, 934 (1987)

View on Pith 1987
[22]

R. Flores-Mendieta, A. Garcia and G. Sanchez-Colon, Ph ys. Rev. D54, 6855 (1996)

View on Pith 1996
[23]

N. Cabibbo, E. C. Swallow and R. Winston, APS-123-QED, h ep-ph/0307214 (2003)

View on Pith 2003
[24]

H. Leutwyler and M. Roos, Z. Phys. C25, 91 (1984)

View on Pith 1984
[25]

E.A. Paschos and U. T¨ urke, Phys. Rep. 178, 145 (1989)

View on Pith 1989
[26]

W. Jaus, Phys. Rev. D44, 2851 (1991)

View on Pith 1991
[27]

P. Post, K. Schilcher, Eur. Phys. J. C25, 427 (2002)

View on Pith 2002
[28]

J. Bijnens and P. Talavera, Nucl. Phys. B 669 , 341 (2003)

View on Pith 2003
[29]

V. Cirigliano, H. Neufeld and H. Pichl, hep-ph/0401173

View on Pith Pith review arXiv
[30]

D. Becirevic et al. , hep-ph/0403217

View on Pith Pith review arXiv
[31]

W.J. Marciano and A. Sirlin, Phys. Rev. Lett. 56, 22 (1986)

View on Pith 1986
[32]

H.H. Williams et al. , Phys. Rev. Lett. 33, 240 (1974); T. Becherrawy et al. , Phys. Rev. D1, 1452 (1970)

View on Pith 1974
[33]

V. Cirigliano, Talk given at 38th Rencontres de Moriond on Electroweak Interactions and Uniﬁed Theories, Les Arcs, France, 15-22 Mar 2003, hep-ph/0 305154

View on Pith 2003
[34]

BNL-E865 Collaboration (A. Sher et al. ), AIP Conf. Proc. 698, 381 (2004), hep- ex/0305042

View on Pith 2004
[35]

B. Sciascia (for the KLOE Collaboration), Talk given at 2nd Workshop on the CKM Unitarity Triangle, Durham, England, 5-9 Apr 2003, eConf C0304052, WG607

View on Pith 2003
[36]

S. Miscetti (for the KLOE Collaboration), Talk given at 39th Rencontres de Moriond: Electroweak Interactions and Uniﬁed Theories La Thuile, Va l d’Aoste, Italy, Mar 21-28 2004, hep-ex/0405040

View on Pith Pith review arXiv 2004
[37]

KTeV Collaboration, (T. Alexopoulos et al. ), hep-ex/0406001

View on Pith Pith review arXiv
[38]

E. Gamiz, M. Jamin, A. Pich, J. Prades and F. Schwab, J. Hi gh Energy Phys. 0301, 060 (2003)

View on Pith 2003
[39]

CDHS Collaboration (H. Abramowicz et al. ), Z. Phys. C15, 19 (1982)

View on Pith 1982
[40]

CCFR Collaboration (A.O. Bazarko et al. ), Z. Phys. C65, 189 (1995)

View on Pith 1995
[41]

CHARM II Collaboration (P. Vilain et al. ), Eur. Phys. J. C11, 19 (1999)

View on Pith 1999
[42]

T. Bolton, KSU-HEP-97-04, hep-ex/9708014 (1997)

View on Pith Pith review arXiv 1997
[43]

FNAL-E531 Collaboration (N. Ushida et al. ), Phys. Lett. B206, 375 (1988)

View on Pith 1988
[44]

CLEO Collaboration (Y. Kubota et al. ), Phys. Rev. D54, 2994 (1996)

View on Pith 1996
[45]

M. Bargiotti et al. , Riv. Nuovo Cim. 23 N3, 1 (2000)

View on Pith 2000
[46]

L. Montanet et al. , Phys. Rev. D50, 1173 (1994) 168 References

View on Pith 1994
[47]

ALEPH Collaboration (R. Barate et al. ), Phys. Lett. B453, 107 (1999); ALEPH Collabo- ration (R. Barate et al. ), ALEPH 99-064 CONF-99-038; ALEPH Collaboration (R. Barat e et al. ), Phys. Lett. B465, 349 (1999)

View on Pith 1999
[48]

DELPHI Collaboration (P. Abreu et al. ), Phys. Lett. B439, 209 (1998)

View on Pith 1998
[49]

OPAL Collaboration (G. Abbiendi et al. ), Phys. Lett. B490, 71 (2000)

View on Pith 2000
[50]

LEP Electroweak Working Group, CERN-EP-2001-098, hep -ex/0112021 (2001)

View on Pith 2001
[51]

K. Benslama (for the CLEO-c Collaboration), Talk given at 37th Rencontres de Moriond on Electroweak Interactions and Uniﬁed Theories, Les Arcs, France, 9-16 Mar 2002, hep- ex/0205003

View on Pith 2002
[52]

N. Isgur and M. Wise, Phys. Lett. B232, 113 (1989); Phys. Lett. 237, 527 (1990)

View on Pith 1989
[53]

H. Georgi, Phys. Lett. B238, 395 (1990)

View on Pith 1990
[54]

M. Luke, Phys. Lett. B252, 447 (1990)

View on Pith 1990
[55]

N. Uraltsev, Talk given at Flavor Physics and CP Violation (FPCP 2003), Paris, France, 3-6 Jun 2003, hep-ph/0309081

View on Pith Pith review arXiv 2003
[56]

M. Shifman, N. Uraltsev and A. Vainshtein, Phys. Rev. D51, 2217 (1995); Erratum-ibid. D52, 3149 (1995)

View on Pith 1995
[57]

M. Neubert, Phys. Lett. B338, 84 (1994)

View on Pith 1994
[58]

A. Falk and M. Neubert, Phys. Rev. D47, 2965 (1993)

View on Pith 1993
[59]

A. Kronfeld, Phys. Rev. D62, 014505 (2000)

View on Pith 2000
[60]

J. Harada et al. , Phys. Rev. D65, 094514 (2002)

View on Pith 2002
[61]

S. Hashimoto et al. , Phys. Rev. D66, 014503 (2002)

View on Pith 2002
[62]

The Heavy Flavor Averaging Group, http://www.slac.st anford.edu/xorg/hfag/ (Summer 2003 and Winter 2004 averages)

View on Pith 2003
[63]

I.I. Bigi, M. Shifman and N.G. Uraltsev, Annu. Rev. Nucl . Part. Sci. 47, 591 (1997)

View on Pith 1997
[64]

I.I. Bigi, M. Shifman, N. Uraltsev and A. Vainshtein, Ph ys. Rev. D56, 4017 (1997); Phys. Rev. D52, 196 (1995)

View on Pith 1997
[65]

CLEO Collaboration (S. Chen et al. ), Phys. Rev. Lett. 87, 251807 (2001)

View on Pith 2001
[66]

C.W. Bauer, Z. Ligeti, M. Luke, A.V. Manohar and M. Trott , Phys. Rev. D70, 094017 (2004)

View on Pith 2004
[67]

K. Schubert, Talk given at 21st International Symposiu m on Lepton and Photon Interac- tions at High Energies (LP 03), Batavia, Illinois, 11-16 Aug 2003

View on Pith 2003
[68]

BABA RCollaboration (B. Aubert et al. ), BABA R-PUB-03-045, hep-ex/0403030

View on Pith Pith review arXiv
[69]

BABA RCollaboration (B. Aubert et al. ), BABA R-CONF-03-034, hep-ex/0403031

View on Pith Pith review arXiv
[70]

BABA RCollaboration (B. Aubert et al. ), BABA R-PUB-04-007, hep-ex/0404017 References 169

View on Pith Pith review arXiv
[71]

BABA RCollaboration (B. Aubert et al. ), Phys. Rev. Lett. 90, 181801 (2003)

View on Pith 2003
[72]

CLEO Collaboration (S.B. Athar et al. ), Phys. Rev. D68, 072003 (2003)

View on Pith 2003
[73]

ARGUS Collaboration (H. Albrecht et al. ), Phys. Lett. B255, 297 (1991)

View on Pith 1991
[74]

CLEO Collaboration (R. Fulton et al. ), Phys. Rev. Lett. 64, 16 (1990)

View on Pith 1990
[75]

CLEO Collaboration (J. Bartelt et al. ), Phys. Rev. Lett. 71, 4111 (1993)

View on Pith 1993
[76]

G. Altarelli, N. Cabibbo, G. Corb` o, L. Maiani and G. Mar tinelli, Nucl. Phys. B208, 365 (1982)

View on Pith 1982
[77]

N. Isgur, D. Scora, B. Grinstein and M.B. Wise, Phys. Rev . D39, 799 (1989)

View on Pith 1989
[78]

J.G. K¨ orner and G.A. Schuler, Z. Phys. C38, 511 (1988); Erratum-ibid. C41, 690 (1989)

View on Pith 1988
[79]

M. Wirbel, B. Stech and M. Bauer, Z. Phys. C29, 637 (1985)

View on Pith 1985
[80]

CLEO Collaboration (A. Bornheim et al. ), Phys. Rev. Lett. 88, 231803 (2002)

View on Pith 2002
[81]

BABA RCollaboration (B. Aubert et al. ), BABAR-CONF-02-012, Contributed to 31st In- ternational Conference on High Energy Physics (ICHEP 2002) , Amsterdam, The Nether- lands, 24-31 Jul 2002, hep-ex/0207081

View on Pith Pith review arXiv 2002
[82]

Belle Collaboration (K. Abe et al. ), BELLE-CONF-0325 (2003), Contributed to Interna- tional Europhysics Conference on High-Energy Physics (HEP 2001), Budapest, Hungary, 12-18 Jul 2001

View on Pith 2003
[83]

A.K. Leibovich, Z. Ligeti and M.B. Wise, Phys. Lett. B539, 242 (2002)

View on Pith 2002
[84]

C.W. Bauer, M. Luke and T. Mannel, Phys. Lett. B543, 261 (2002)

View on Pith 2002
[85]

M. Neubert, Phys. Lett. B543, 269 (2002)

View on Pith 2002
[86]

C.N. Burrell, M.E. Luke and A.R. Williamson, Phys.Rev. D69, 074015 (2004)

View on Pith 2004
[87]

I.I.Y. Bigi and N. Uraltsev, Int. J. Mod. Phys. A16, 5201 (2001)

View on Pith 2001
[88]

M.B. Voloshin, Phys. Lett. B515, 74 (2001)

View on Pith 2001
[89]

DELPHI Collaboration (P. Abreu et al. ), Phys. Lett. B478, 14 (2000)

View on Pith 2000
[90]

BABA RCollaboration (B. Aubert et al. ), Phys. Rev. Lett. 92, 071802 (2004)

View on Pith 2004
[91]

CLEO Collaboration (A. Bornheim et al.), CLEO-CONF-02-08, Contributed to 31st Inter- national Conference on High Energy Physics (ICHEP 2002), Am sterdam, The Netherlands, 24-31 Jul 2002, hep-ex/0207064

View on Pith Pith review arXiv 2002
[92]

A. Sugiyama (for the Belle Collaboration), Talk given a t 38th Rencontres de Moriond on Electroweak Interactions and Uniﬁed Theories, Les Arcs, Fr ance, 15-22 Mar 2003, hep- ex/0306020

View on Pith 2003
[93]

ALEPH collaboration (R. Barate et al. ), Eur. Phys. J. C6, 555 (1999)

View on Pith 1999
[94]

OPAL collaboration, (G. Abbiendi et al. ), Eur. Phys. J. C21, 399 (2001) 170 References

View on Pith 2001
[95]

L. Gibbons (for the CLEO Collaboration), To appear in th e proceedings of 9th Interna- tional Conference on B Physics at Hadron Machines (Beauty 2003), Pittsburgh, Penn syl- vania, 14-18 Oct 2003, hep-ex/0402009

View on Pith Pith review arXiv 2003
[96]

O. Cat` a and S. Peris, hep-ph/0406094

View on Pith Pith review arXiv
[97]

T. Trippe, private communication (2004)

View on Pith 2004
[98]

KTeV Collaboration, (T. Alexopoulos et al. ), hep-ex/0406002

View on Pith Pith review arXiv
[99]

L. Lellouch, Nucl. Phys. Proc. Suppl. 94, 142 (2001)

View on Pith 2001
[100]

J. Bijnens and J. Prades, Nucl. Phys. B444, 523 (1995); J. High Energy Physics 01, 002 (2000); S. Peris and E. de Rafael, Phys. Rev. Lett. 490, 213 (2000)

View on Pith 1995
[101]

G. Buchalla, A.J. Buras and M.E. Lautenbacher, Rev. Mo d. Phys. 68, 1125 (1996)

View on Pith 1996
[102]

T. Inami and C.S. Lim, Prog. Theor. Phys. 65, 297 (1981); Erratum-ibid. 65, 1772 (1981)

View on Pith 1981
[103]

L. Cerrito (for the CDF and D0 Collaboration), To appea r in the proceedings of 39th Rencontres de Moriond on QCD and High-Energy Hadronic Inter actions, La Thuile, Italy, 28 Mar - 4 Apr 2004, hep-ex/0405046

View on Pith Pith review arXiv 2004
[104]

K. Melnikov, T. van Ritbergen, Phys. Lett. B482, 99 (2000)

View on Pith 2000
[105]

N. Gray, D.J. Broadhurst, W. Grafe and K. Schilcher, Z. Phys. C48, 673 (1990)

View on Pith 1990
[106]

D.J. Broadhurst, N. Gray and K. Schilcher, Z. Phys. C52, 111 (1991)

View on Pith 1991
[107]

S. Herrlich and U. Nierste, Nucl. Phys. B419, 292 (1994)

View on Pith 1994
[108]

U. Nierste, Ref. [ 9] and private communication (2003)

View on Pith 2003
[109]

D. Becirevic, Talk given at 2nd Workshop on the CKM Unit arity Triangle, Durham, England, 5-9 Apr 2003, hep-ph/0310072

View on Pith Pith review arXiv 2003
[110]

M.J. Booth, Phys. Rev. D51, 2338 (1995)

View on Pith 1995
[111]

S.R. Sharpe and Y. Zhang, Phys. Rev. D53, 5125 (1996)

View on Pith 1996
[112]

C. Bernard, T. Blum and A. Soni, Phys. Rev. D58 014501 (1998)

View on Pith 1998
[113]

JLQCD Collaboration (N. Yamada et al. ), Nucl. Phys. B Proc. Suppl. 106, 397 (2002), hep-lat/0110087

View on Pith Pith review arXiv 2002
[114]

S. Kronfeld and S.M. Ryan, Phys. Lett. B543, 59 (2002)

View on Pith 2002
[115]

D. Becirevic et al. , Phys. Lett. B563, 150 (2003)

View on Pith 2003
[116]

C. Davies, Talk given at Flavor Physics and CP Violation (FPCP 2003), Paris, France, 3-6 Jun 2003, hep-ph/0311040

View on Pith Pith review arXiv 2003
[117]

J.L. Rosner, Nucl. Instrum. Meth. A462, 304 (2001)

View on Pith 2001
[118]

ALEPH Collaboration (A. Heister et al. ), Eur. Phys. J. C29, 143 (2003) References 171

View on Pith 2003
[119]

DELPHI Collaboration (P. Abreu et al. ), Eur. Phys. J. C16, 555 (2000); DELPHI Collab- oration (P. Abreu et al. ), Eur. Phys. J. C18, 229 (2000); DELPHI Collaboration (J. Ad- ballah et al. ), Eur. Phys. J. C28, 155 (2003); DELPHI Collaboration (J. Adballah et al. ), Contribution 607 to 30th International Conference on High- Energy Physics (ICHEP 2002), Am...

View on Pith 2000
[120]

OPAL Collaboration (G. Abbiendi et al. ), Eur. Phys. J. C11 587, (1999); OPAL Collab- oration (G. Abbiendi et al. ), Eur. Phys. J. C19, 241 (2001)

View on Pith 1999
[121]

SLD Collaboration (K. Abe et al. ), Phys. Rev. D66, 032009 (2002); SLD Collaboration (K. Abe et al. ), Phys. Rev. D67, 012006 (2003); SLD Collaboration (K. Abe et al. ), SLAC-PUB-8568, Contributed to 30th International Confere nce on High-Energy Physics (ICHEP 2000), Osaka, Japan, 27 Jul - 2 Aug 2000, hep-ex/00120 43

View on Pith 2002
[122]

CDF Collaboration (F. Abe et al. ), Phys. Rev. Lett. 82, 3576 (1999)

View on Pith 1999
[123]

H.G. Moser and A. Roussarie, Nucl. Inst. Meth. A384, 491 (1997)

View on Pith 1997
[124]

D. Abbaneo and G. Boix, J. High Energy Phys. 08, 4 (1999)

View on Pith 1999
[125]

P. Checchia, E. Piotto and F. Simonetto, Contributed t o International Europhysics Con- ference on High-Energy Physics (EPS-HEP 99), Tampere, Finl and, 15-21 Jul 1999, hep- ph/9907300

View on Pith 1999
[126]

A. Ali and M. Misiak, Chapter 6.2 in Ref. [ 9]

View on Pith
[127]

M. Iwasaki (for the Belle Collaboration), Talk given a t 39th Rencontres de Moriond: Electroweak Interactions and Uniﬁed Theories La Thuile, Va l d’Aoste, Italy, 21-28 Mar 2004

View on Pith 2004
[128]

A. Ali, E. Lunghi and A.Y. Parkhomenko, DESY-04-065, h ep-ph/0405075 (2004)

View on Pith 2004
[129]

BABA RCollaboration (B. Aubert et al. ), Phys. Rev. Lett. 89, 201802 (2002)

View on Pith 2002
[130]

Belle Collaboration (K. Abe et al.), BELLE-CONF-0344, Contributed to 21st International Symposium on Lepton and Photon Interactions at High Energie s (LP 03), Batavia, Illinois, 11-16 Aug 2003, hep-ex/0308036

View on Pith Pith review arXiv 2003
[131]

R. Fleischer, Phys. Lett. B365, 399 (1996)

View on Pith 1996
[132]

D. London and A. Soni, Phys. Lett. B407, 61(1997); see also Ref. [ 201]

View on Pith 1997
[133]

Y. Grossman, Z. Ligeti, Y. Nir and H. Quinn Phys. Rev. D68, 015004 (2003)

View on Pith 2003
[134]

M. Gronau, Y. Grossman and J.L. Rosner, Phys. Lett. B579, 331 (2004)

View on Pith 2004
[135]

M. Beneke and M. Neubert, Nucl. Phys. B675 333 (2003)

View on Pith 2003
[136]

BABA RCollaboration (B. Aubert et al. ), BABA R-PUB-04/004, hep-ex/0403026 (2004)

View on Pith Pith review arXiv 2004
[137]

Belle Collaboration (K. Abe et al. ), Phys. Rev. Lett. 91, 261602 (2003)

View on Pith 2003
[138]

M. Verderi (for the BABA RCollaboration), Talk given at 39th Rencontres de Moriond: Electroweak Interactions and Uniﬁed Theories La Thuile, Va l d’Aoste, Italy, 21-28 Mar 2004 172 References

View on Pith 2004
[139]

BABA RCollaboration (B. Aubert et al. ), BABA R-PUB-04-017, hep-ex/0406040 (2004)

View on Pith Pith review arXiv 2004
[140]

BABA RCollaboration (B. Aubert et al. ), Phys. Rev. Lett. 91, 161801 (2003)

View on Pith 2003
[141]

M. Gronau and D. London, Phys. Rev. Lett. 65, 3381 (1990)

View on Pith 1990
[142]

Y. Grossman and H.R. Quinn, Phys. Rev. D58, 017504 (1998)

View on Pith 1998
[143]

J. Charles, Th` ese de l’Universit´ e Paris-Sud, April1999, LPT-Orsay 99-31; available (in French) at http://www.tel.ccsd.cnrs.fr (ID 00002502)

View on Pith
[144]

M. Gronau, D. London, N. Sinha and R. Sinha, Phys. Lett. B514, 315 (2001)

View on Pith 2001
[145]

BABA RCollaboration (B. Aubert et al. ), BABA R-PUB-04-09, hep-ex/0404029 (2004)

View on Pith Pith review arXiv 2004
[146]

BABA RCollaboration (B. Aubert et al. ), Phys. Rev. D69, 031102 (2004)

View on Pith 2004
[147]

BABA RCollaboration (B. Aubert et al. ), Phys. Rev. Lett. 91, 171802 (2003)

View on Pith 2003
[148]

Belle Collaboration (J. Zhang et al. ), Phys. Rev. Lett. 91, 221801 (2003)

View on Pith 2003
[149]

L. Roos (for the BABA RCollaboration), Talk given at 39th Rencontres de Moriond: E lec- troweak Interactions and Uniﬁed Theories La Thuile, Val d’A oste, Italy, 21-28 Mar 2004

View on Pith 2004
[150]

CMD-2 Collaboration (R. Akhmetshin et al. ) Phys. Lett. B578, 285 (2004)

View on Pith 2004
[151]

ALEPH Collaboration (R. Barate et al. ), Z. Phys. C76, 15 (1997)

View on Pith 1997
[152]

A. Falk, Z. Ligeti, Y. Nir and H. R. Quinn, Phys. Rev. D69, 011502 (2004)

View on Pith 2004
[153]

BABA RCollaboration (B. Aubert et al. ), BABA R-CONF-03-004, Contributed to 38th Ren- contres de Moriond on Electroweak Interactions and Uniﬁed T heories, Les Arcs, France, 15-22 Mar 2003, hep-ex/0304030

View on Pith Pith review arXiv 2003
[154]

Belle Collaboration, (K. Abe et al. ), BELLE-CONF-0247, Contributed to 31st Interna- tional Conference on High Energy Physics (ICHEP 2002), Amst erdam, The Netherlands, 24-31 Jul 2002

View on Pith 2002
[155]

Y. Nir, Nucl. Phys. Proc. Suppl. 117, 111 (2003), hep-ph/0208080

View on Pith Pith review arXiv 2003
[156]

Y. Grossman and H. R. Quinn, Phys. Rev. D56, 7259 (1997)

View on Pith 1997
[157]

LASS Collaboration (D. Aston et al. ), Nucl. Phys. B296, 493 (1988)

View on Pith 1988
[158]

J. Charles et al. , Phys. Lett. B425, 375 (1998); Erratum-ibid. B433, 441 (1998)

View on Pith 1998
[159]

C.W. Chiang and L. Wolfenstein, Phys. Rev. D61, 074031 (2000)

View on Pith 2000
[160]

A.S. Dighe, I. Dunietz and R. Fleischer, Eur. Phys. J. C6, 647 (1999)

View on Pith 1999
[161]

B. Kayser, in Proceedings of the 32nd Rencontres de Mor iond on Electroweak Interactions and Uniﬁed Theories, Les Arcs, France, edited by J. Trˆ an Tha nh Vˆ an, Ed. Fronti` eres (1997), p.389; Y.I. Azimov, JETP Lett. 50, 447 (1989); Phys. Rev. D42, 3705 (1990)

View on Pith 1997
[162]

H.R. Quinn, T. Schietinger, J.P. Silva and A.E. Snyder , Phys. Rev. Lett. 85, 5284 (2000)

View on Pith 2000
[163]

Y. Grossman and D. Pirjol, J. High Energy Phys. 006, 029 (2000) References 173

View on Pith 2000
[164]

A.J. Buras and M. Jamin, J. High Energy Phys. 0401, 048 (2004)

View on Pith 2004
[165]

A. J. Buras, F. Schwab and S. Uhlig, TUM-HEP-547, MPP-2 004-47, hep-ph/0405132 (2004)

View on Pith Pith review arXiv 2004
[166]

NA31 Collaboration (G.D. Barr et al. ), Phys. Lett. B317, 233 (1993)

View on Pith 1993
[167]

E731 Collaboration (L.K. Gibbons et al. ), Phys. Rev. D55, 6625 (1997)

View on Pith 1997
[168]

NA48 Collaboration (J.R. Batley et al. ), Phys. Lett. B544, 97 (2002)

View on Pith 2002
[169]

KTeV Collaboration (A. Alavi-Harati et al. ), Phys. Rev. D67, 012005 (2003)

View on Pith 2003
[170]

A. Buras, M. Jamin and M.E. Lautenbacher, Nucl. Phys. B408, 209 (1993)

View on Pith 1993
[171]

M. Ciuchini, E. Franco, G. Martinelli and L. Reina, Phy s. Lett. B301, 263 (1993)

View on Pith 1993
[172]

E. Pallante, A. Pich and I. Scimemi, Nucl. Phys. B617, 441 (2001)

View on Pith 2001
[173]

T. Hambye, S. Peris and E. de Rafael, J. High Energy Phys . 0305, 027 (2003)

View on Pith 2003
[174]

J. Bijnens, E. Gamiz and J. Prades, J. High Energy Phys. 0110, 009 (2001)

View on Pith 2001
[175]

D. Becirevic (for the SPQCDR Collaboration), Nucl. Ph ys. Proc. Suppl. 119, 359 (2003), hep-lat/0209136

View on Pith Pith review arXiv 2003
[176]

CP-PACS Collaboration (S. Aoki et al. ), Nucl. Phys. Proc. Suppl. 106, 332 (2002)

View on Pith 2002
[177]

RBC Collaboration (T. Blum et al. ), Phys. Rev. D68, 114506 (2003)

View on Pith 2003
[178]

M. Golterman and S. Peris, Phys. Rev. D68, 094506 (2003)

View on Pith 2003
[179]

E. Gamiz, J. Prades and I. Scimemi, J. High Energy Phys. 0310, 042 (2003)

View on Pith 2003
[180]

G. Buchalla and A. Buras, Nucl. Phys. B548, 309 (1999)

View on Pith 1999
[181]

W.J. Marciano and Z. Parsa, Phys. Rev. D53, 1 (1996)

View on Pith 1996
[182]

The CKM Collaboration, Proposal to the FNAL PAC, http://www.fnal.gov/projects/ckm/documentation/public/proposal/proposal.html

View on Pith
[183]

T. Inagaki (for the E391 Collaboration), KEK-PREPRIN T-96-181, Talk given at 3rd International Workshop on Particle Physics Phenomenology , Taipei, Taiwan, 14-17 Nov 1996

View on Pith 1996
[184]

The KOPIO Collaboration, RSVP MRE Proposal, http://pubweb.bnl.gov/people/rsvp/proposal.ps

View on Pith
[185]

BABA RCollaboration (B. Aubert et al. ), BABA R-PUB-03-031, hep-ex/0309017 (2003)

View on Pith Pith review arXiv 2003
[186]

Belle Collaboration (P. Krokovny et al. ), Phys. Rev. Lett. 89, 231804 (2002); BABA R Collaboration (B. Aubert et al.), BABAR-CONF-02-034 Contributed to 31st International Conference on High Energy Physics (ICHEP 2002), Amsterdam, The Netherlands, 24-31 Jul 2002, hep-ex/0207053

View on Pith Pith review arXiv 2002
[187]

BABA RCollaboration (B. Aubert et al. ), BABA R-PUB-03-033, hep-ex/0310037 (2003) 174 References

View on Pith Pith review arXiv 2003
[188]

Belle Collaboration (K. Abe et al.), BELLE-CONF-0341, Contributed to 21st International Symposium on Lepton and Photon Interactions at High Energie s (LP 03), Batavia, Illinois, 11-16 Aug 2003, hep-ex/0308048

View on Pith Pith review arXiv 2003
[189]

M. Gronau and D. London, Phys. Lett. B253, 483 (1991)

View on Pith 1991
[190]

M. Gronau and D. Wyler, Phys. Lett. B265, 172 (1991)

View on Pith 1991
[191]

I. Dunietz, Phys. Lett. B270, 75 (1991)

View on Pith 1991
[192]

I. Dunietz, Z. Phys. C56, 129 (1992)

View on Pith 1992
[193]

D. Atwood, I. Dunietz and A. Soni, Phys. Rev. Lett. 78, 3257 (1997); Phys. Rev. D63, 036005 (2001)

View on Pith 1997
[194]

BABA RCollaboration (B. Aubert et al. ), BABA R-PUB-04-002, hep-ex/0402024 (2004)

View on Pith Pith review arXiv 2004
[195]

A. Giri, Y. Grossman, A. Soﬀer and J. Zupan, Phys. Rev. D68, 054018 (2003)

View on Pith 2003
[196]

Belle Collaboration (K. Abe et al.), BELLE-CONF-0343, hep-ex/0308043 (2003); updated analysis presented by A. Poluektof (for the Belle Collabora tion) at 39th Rencontres de Moriond: Electroweak Interactions and Uniﬁed Theories La T huile, Val d’Aoste, Italy, Mar 21-28, 2004

View on Pith Pith review arXiv 2003
[197]

Belle Collaboration (K. Abe et al. ), BELLE-CONF-0343, hep-ex/0406067 (2004)

View on Pith Pith review arXiv 2004
[198]

CLEO Collaboration (H. Muramatsu et al.), Phys. Rev. Lett. 89, 251802 (2002); Erratum- ibid. 90, 059901 (2003); CLEO Collaboration (S. Kopp et al. ), Phys. Rev. D63, 092001 (2001)

View on Pith 2002
[199]

J. Ha ¨ ıssinski, 21st Ecole de Gif (1989), in English, a nd references therein

View on Pith 1989
[200]

M. Pivk, Th` ese de l’Universit´ e Paris VII, May 2003, BABA R-THESIS-03/012, available (in French) at http://tel.ccsd.cnrs.fr (ID 0000 2991)

View on Pith 2003
[201]

BABA R Collaboration (P.F Harrison and H. Quinn eds.), “The BABA R Physics Book: Physics at an Asymmetric B Factory”, SLAC-R-0504 (1998)

View on Pith 1998
[202]

J. Charles, Phys. Rev. D59 054007, (1999)

View on Pith 1999
[203]

S. Gardner, Phys. Rev. D59, 077502 (1999)

View on Pith 1999
[204]

A. H¨ ocker, H. Lacker, M. Pivk and L. Roos, LAL 02-103 (2 002), LPNHE 2002-15; writeup available at http://www.slac.stanford.edu/xorg/ckmﬁtter/ckm talks.html

View on Pith 2002
[205]

M. Gronau and J.L. Rosner, Phys. Rev. D65, 013004 (2002); Erratum-ibid. D65, 079901 (2002)

View on Pith 2002
[206]

R. Fleischer and T. Mannel, Phys. Lett. B397, 269 (1997)

View on Pith 1997
[207]

M. Beneke, G. Buchalla, M. Neubert and C.T. Sachrajda, Phys. Rev. Lett. 83, 1914 (1999)

View on Pith 1999
[208]

M. Beneke, G. Buchalla, M. Neubert and C.T. Sachrajda, Nucl. Phys. B606, 245 (2001)

View on Pith 2001
[209]

M. Pivk and F.R. Le Diberder, LAL 04-10, hep-ph/040626 3, Eur. Phys. J. C39, 397 (2005) References 175

View on Pith 2005
[210]

A.J. Buras and R. Fleischer, Eur. Phys. J. C11, 93 (1999)

View on Pith 1999
[211]

M. Neubert and J.L. Rosner, Phys. Lett. B441, 403 (1998); Phys. Rev. Lett. 81, 5076 (1998)

View on Pith 1998
[212]

J.P. Silva and L. Wolfenstein, Phys. Rev. D49, 1151 (1994)

View on Pith 1994
[213]

R. Fleischer, Phys. Lett. B459, 306 (1999)

View on Pith 1999
[214]

J.D. Bjorken in “New Developments in High Energy Physics” , eds. E.G Floratos and A. Verganelakis, Nucl. Phys. B11 (Proc. Suppl.), 325 (1989)

View on Pith 1989
[215]

M. Neubert and B. Stech, Adv. Ser. Direct. High Energy P hys. 15 294 (1998)

View on Pith 1998
[216]

Y.Y. Keum, H. Li, A.I. Sanda Phys. Lett. B504, 6 (2001)

View on Pith 2001
[217]

M. Ciuchini et al. , Phys. Lett. B515, 33 (2001)

View on Pith 2001
[218]

C.W. Bauer, D. Pirjol, I.Z. Rothstein and I.W. Stewart , MIT-CTP-3469, hep-ph/0401188 (2004)

View on Pith Pith review arXiv 2004
[219]

H. Jawahery, Talk given at 21st International Symposi um on Lepton and Photon Interac- tions at High Energies (LP 03), Batavia, Illinois, 11-16 Aug 2003

View on Pith 2003
[220]

Belle Collaboration (K. Abe et al. ), BELLE-PREPRINT-2004-1, hep-ex/0401029 (2004)

View on Pith Pith review arXiv 2004
[221]

T. Browder, Talk given at 21st International Symposiu m on Lepton and Photon Interac- tions at High Energies (LP 03), Batavia, Illinois, 11-16 Aug 2003

View on Pith 2003
[222]

BABA RCollaboration (B. Aubert et al. ), Phys. Rev. Lett. 91, 021801 (2003)

View on Pith 2003
[223]

T. Tomura (for the Belle Collaboration), Proceedings of 38th Rencontres de Moriond on Electroweak Interactions and Uniﬁed Theories, Les Arcs, Fr ance, 15-22 Mar 2003, hep- ex/0305036

View on Pith 2003
[224]

J. Fry, Talk given at 21st International Symposium on L epton and Photon Interactions at High Energies (LP 03), Batavia, Illinois, 11-16 Aug 2003

View on Pith 2003
[225]

CLEO Collaboration (S. Chen et al. ), Phys. Rev. Lett.85, 525 (2000)

View on Pith 2000
[226]

M. Bona (for the BABA RCollaboration), Talk given at Flavor Physics and CP Violation (FPCP 2003), Paris, France, 3-6 Jun 2003

View on Pith 2003
[227]

BABA RCollaboration (B. Aubert et al. ), Phys. Rev. Lett. 89, 281802 (2001)

View on Pith 2001
[228]

Belle Collaboration (Y. Chao et al.), BELLE-PREPRINT-2003-26, hep-ex/0311061 (2003)

View on Pith Pith review arXiv 2003
[229]

CLEO Collaboration (A. Bornheim et al. ), Phys. Rev. D68, 052002 (2003)

View on Pith 2003
[230]

BABA RCollaboration (B. Aubert et al. ), Phys. Rev. Lett. 91, 241801 (2003)

View on Pith 2003
[231]

CDF Collaboration (C. Paus et al. ), Results prepared for Summer conferences (2003), http://www-cdf.fnal.gov/physics/new/bottom/030529.blessed-bhh/

View on Pith 2003
[232]

A.J. Buras, R. Fleischer, S. Recksiegel and F. Schwab, Phys. Rev. Lett. 92, 101804 (2004); A.J. Buras, R. Fleischer, S. Recksiegel and F. Schwab, CERN- PH-TH-2004-020, hep- ph/0402112 (2004) 176 References

View on Pith 2004
[233]

S. Barshay, L.M. Sehgal and J. van Leusen, Phys. Lett. B591, 97 (2004); A. Ali, E. Lunghi and A.Ya. Parkhomenko, DESY-04-036, hep-ph/0403275 (2004 ); M. Gronau and J.L. Ros- ner, TECHNION-PH-2004-21, hep-ph/0405173 (2004); G. Buch alla and A. Salim Saﬁr, LMU-24-03, hep-ph/0406016 (2004)

View on Pith Pith review arXiv 2004
[234]

L. Roos, Talk given at 2nd Workshop on the CKM Unitarity Triangle, Durham, England, 5-9 Apr 2003, eConf C0304052, WG418

View on Pith 2003
[235]

C.-W. Chiang, M. Gronau, J.L. Rosner and D.A. Suprun, M ADPH-04-1372, hep- ph/0404073 (2004)

View on Pith 2004
[236]

D. Pirjol, Phys. Rev. D60, 054020 (1999)

View on Pith 1999
[237]

M. Gronau and J.L. Rosner, Phys. Rev. D59, 113002 (1999); H.J. Lipkin, Phys. Lett. B445, 403 (1999); J. Matias, Phys. Lett. B520, 131 (2001)

View on Pith 1999
[238]

M. Gronau and J.L. Rosner, Phys. Lett. B572, 43 (2003)

View on Pith 2003
[239]

A.J. Buras, R. Fleischer, S. Recksiegel and F. Schwab, Eur. Phys. J. C32, 45 (2003)

View on Pith 2003
[240]

V. Barger, C.-W. Chiang, P. Langacker, H.S. Lee, MADPH -04-1381, hep-ph/0406126 (2004)

View on Pith Pith review arXiv 2004
[241]

Y. Nir and H.R. Quinn, Phys. Rev. Lett. 67, 541 (1991)

View on Pith 1991
[242]

L. Lavoura, Mod. Phys. Lett. A7, 1553 (1992)

View on Pith 1992
[243]

M. Imbeault, A. St-Laurent Lemerle, V. Page and D. Lond on, Phys. Rev. Lett. 92, 081801 (2004)

View on Pith 2004
[244]

M. Gronau, O.F. Hernandez, D. London and J.L. Rosner, P hys. Rev. D52, 6374 (1995)

View on Pith 1995
[245]

M. Gronau and J.L. Rosner, CLNS 03/1852, TECHNION-PH- 2003-41, To appear in the proceedings of Workshop on the Discovery Potential of an Asy mmetricB Factory at 10 36 Luminosity, Menlo Park, California, 8-10 May 2003, hep-ph/ 0311280 (2003)

View on Pith 2003
[246]

M. Gronau, D. Pirjol and T.M. Yan, Phys. Rev. D60, 034021 (1999); Erratum-ibid. D69, 119901 (2004)

View on Pith 1999
[247]

BABA RCollaboration (B. Aubert et al. ), Phys. Rev. Lett. 91, 201802 (2003); updated results BABA R-PLOT-0055 (2003)

View on Pith 2003
[248]

D. Du, J. Sun, G. Zhu and D. Du, Phys. Rev. D68, 054003 (2003) D. Du, J. Sun, D. Yang and G. Zhu, Phys. Rev. D67, 014023 (2003); D. Du, H. Gong, J. Sun, D. Yang and G. Zhu Phys. Rev. D65, 094025 (2002); Erratum-ibid. D66, 079904 (2002)

View on Pith 2003
[249]

R. Aleksan, P.-F. Giraud, V. Mor´ enas, O. P` ene and A. S . Saﬁr, Phys. Rev. D67, 094019 (2003)

View on Pith 2003
[250]

N. de Groot, W.N. Cottingham and I.B. Whittingham, Con tributed to 38th Rencontres de Moriond on QCD and Hadronic Interactions, Les Arcs, Franc e, 22-29 Mar 2003, hep- ph/0305263 eConf C0304052, WG405

View on Pith 2003
[251]

C.-W. Chiang, M. Gronau, Z. Luo, J.L. Rosner and D.A. Su prun, Phys. Rev. D69, 034001 (2004) References 177

View on Pith 2004
[252]

A. H¨ ocker, M. Laget, S. Laplace and J. von Wimmersperg -Toeller, LAL 03-17 (2003), writeup available at http://www.slac.stanford.edu/xorg /ckmﬁtter/ckm talks.html

View on Pith 2003
[253]

H.R. Quinn and A.E. Snyder, Phys. Rev. D48, 2139 (1993)

View on Pith 1993
[254]

S. Versill´ e, Th` ese de l’Universit´ e Paris-Sud, April 1999; available (in French) at http://www-lpnhep.in2p3.fr/bab ar/public/versille/Thesis/

View on Pith 1999
[255]

Belle Collaboration, (K. Abe et al. ), BELLE-CONF-0318, Contributed to International Europhysics Conference on High-Energy Physics (HEP 2001), Budapest, Hungary, 12-18 Jul 2001

View on Pith 2001
[256]

CLEO Collaboration (C.P. Jessop et al. ), Phys. Rev. Lett. 85, 2881 (2000)

View on Pith 2000
[257]

BABA RCollaboration, (B. Aubert et al. ), BABA R-PUB-03-037, hep-ex/0311049 (2003)

View on Pith Pith review arXiv 2003
[258]

BABA RCollaboration, (B. Aubert et al. ), BABA R-CONF-03-14, Contributed to Interna- tional Europhysics Conference on High-Energy Physics (HEP 2003), Aachen, Germany, 17-23 Jul 2003, hep-ex/0307087

View on Pith Pith review arXiv 2003
[259]

Belle Collaboration (J. Zhang et al. ), Belle-PREPRINT-2004-15, hep-ex/0406006 (2004)

View on Pith Pith review arXiv 2004
[260]

Belle Collaboration (J. Dragic et al. ), BELLE-PREPRINT-2004-14, hep-ex/0405068 (2004)

View on Pith Pith review arXiv 2004
[261]

Belle Collaboration (K. Abe et al. ), BELLE-CONF-0317, Contributed to International Europhysics Conference on High-Energy Physics (HEP 2003), Aachen, Germany, 17-23 Jul 2003

View on Pith 2003
[262]

CLEO Collaboration (E. Eckhart et al. ), Phys. Rev. Lett. 89, 251801 (2002)

View on Pith 2002
[263]

CLEO Collaboration (D.M. Asner et al. ), Phys. Rev. D53, 1039 (1996)

View on Pith 1996
[264]

BABA RCollaboration (B. Aubert et al. ), BABA R-PUB-03-027, hep-ex/0308065 (2003)

View on Pith Pith review arXiv 2003
[265]

Belle Collaboration (K. Abe et al.), BELLE-CONF-0338, Contributed to 21st International Symposium on Lepton and Photon Interactions at High Energie s (LP 03), Batavia, Illinois, 11-16 Aug 2003

View on Pith 2003
[266]

R. Aleksan, F. Buccella, A. Le Yaouanc, L. Oliver, O. P` ene and J.-C. Raynal Phys. Lett. B356, 96 (1995)

View on Pith 1995
[267]

H.J. Lipkin, Y. Nir, H.R. Quinn and A. Snyder, Phys. Rev . D44, 1454 (1991)

View on Pith 1991
[268]

H.R. Quinn and J. Silva, Phys. Rev. D62, 054002 (2000)

View on Pith 2000
[269]

I. Dunietz, H.R. Quinn, A. Snyder, W. Toki and H.J. Lipk in, Phys. Rev. D43, 2193 (1991); A.S. Dighe, I. Dunietz, HJ. Lipkin and J.L. Rosner, Phys. Let t. B369, 144 (1996)

View on Pith 1991
[270]

A.L. Kagan, UCTP-102-04, hep-ph/0405134 (2004)

View on Pith Pith review arXiv 2004
[271]

J. Charles, A. Le Yaouanc, L. Oliver, O. P` ene and J.C. R aynal, Phys. Rev. D60, 014001 (1999)

View on Pith 1999
[272]

M. Zito, Phys. Lett. B586, 314 (2004) 178 References

View on Pith 2004
[273]

M. Ciuchini, E. Franco, G. Martinelli and L. Silvestri ni, Nucl. Phys. B501, 271 (1997); M. Ciuchini, R Contino, E. Franco, G. Martinelli and L. Silve strini, Nucl. Phys. B512, 3 (1998); Erratum-ibid. B531, 656 (1998); M. Ciuchini, E. Franco, G. Martinelli, M. Pieri ni and L. Silvestrini, Phys. Lett. B515, 33 (2001); A. Khodjamirian, Th. Mannel and B. Mel...

View on Pith 1997
[274]

J.F. Donoghue, E. Golowich, A.A. Petrov and J.M. Soare s, Phys. Rev. Lett. 77, 2178 (1996)

View on Pith 1996
[275]

See, e.g., Ref. [ 278] and references therein

View on Pith
[276]

R. Fleischer, G. Isidori and J. Matias, J. High Energy P hys. 0305, 053 (2003)

View on Pith 2003
[277]

J.M. Soares and L. Wolfenstein, Phys. Rev. D47, 1021 (1993)

View on Pith 1993
[278]

Y. Grossman, Y. Nir and M.P. Worah, Phys. Lett. B407, 307 (1997)

View on Pith 1997
[279]

A.L. Kagan and M. Neubert, Phys. Lett. B492, 115 (2000)

View on Pith 2000
[280]

R. Fleischer and T. Mannel, Phys. Lett. B506, 311 (2001)

View on Pith 2001
[281]

D. Atwood and G. Hiller, LMU-09-03, hep-ph/0307251 (2 003)

View on Pith Pith review arXiv
[282]

S. Laplace, Z. Ligeti, Y. Nir and G. Perez, Phys. Rev. D65, 094040 (2002)

View on Pith 2002
[283]

A.I. Sanda, and Z-z. Xing, Phys. Rev. D56, 6866 (1997)

View on Pith 1997
[284]

L. Randall and S. Su, Nucl. Phys. B540, 37 (1999)

View on Pith 1999
[285]

R.N. Cahn and M.P. Worah, Phys. Rev. D60, 076006 (1999)

View on Pith 1999
[286]

G. Barenboim, G. Eyal and Y. Nir, Phys. Rev. Lett. 83, 4486 (1999)

View on Pith 1999
[287]

M. Beneke, G. Buchalla, A. Lenz and U. Nierste, Phys. Le tt. B 576 173 (2003)

View on Pith 2003
[288]

M. Ciuchini, E. Franco, V. Lubicz, F. Mescia and C. Tara ntino, JHEP 0308 031 (2003)

View on Pith 2003
[289]

OPAL Collaboration (G. Abbiendi et al. ), Eur. Phys. J. C12, 609 (2000)

View on Pith 2000
[290]

CLEO Collaboration (D.E. Jaﬀe et al. ), Phys. Rev. Lett. 86, 5000 (2001)

View on Pith 2001
[291]

ALEPH Collaboration (R. Barate et al. ), Eur. Phys. J. C20, 431 (2001)

View on Pith 2001
[292]

BABA RCollaboration (B. Aubert et al. ), Phys. Rev. Lett. 88, 231801 (2002)

View on Pith 2002
[293]

BABA RCollaboration (B. Aubert et al. ), Phys. Rev. Lett. 92, 181801 (2004)

View on Pith 2004
[294]

G.C. Branco, F. Cagarrinho, F. Kr¨ uger, Phys. Lett. B459 224, (1999)

View on Pith 1999
[295]

M. Ciuchini, G. Degrassi, P. Gambino and G.F. Giudice, Nucl. Phys. B534, 3 (1998); A. Ali and D. London, Eur. Phys. J. C9, 687 (1999); A. Ali and D. London Phys. Rept. 320, 79 (1999; A.J. Buras, P. Gambino, M. Gorbahn, S. Jager and L. Silvestrini, Phys. Lett. B500, 161 (2001); A. J. Buras, P. Gambino, M. Gorbahn, S. Jager and L. Silvestrini, Nucl. Phys. B...

View on Pith 1998
[296]

For recent references see, e.g., Y. Grossman, Int. J. M od. Phys. A19, 907 (2004); M. Neu- bert, CLNS-04-1878, hep-ph/0405105 (2004)

View on Pith Pith review arXiv 2004
[297]

C.W. Chiang and J. Rosner, Phys. Rev. D68, 014007 (2003)

View on Pith 2003
[298]

Y. Grossman, G. Isidori and M.P. Worah, Phys. Rev. D58, 057504 (1998); R. Fleischer and T. Mannel, Phys. Lett. B511, 240 (2001); M. Ciuchini and L. Silvestrini, Phys. Rev. Lett. 89, 231802 (2002); see also Ref. [ 300]

View on Pith 1998
[299]

Y. Grossman, A.L. Kagan and Z. Ligeti Phys. Lett. B538, 327 (2002)

View on Pith 2002
[300]

G. Hiller, Phys. Rev. D66, 071502 (2002)

View on Pith 2002

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Two-Loop Electroweak Corrections for the K -> pi nu anti-nu Decays
hep-ph 2010-09 conditional novelty 7.0 of 10

Full two-loop electroweak corrections to X_t are computed, reducing the electroweak theory error on the K -> pi nu nu branching ratios from about 2% to about 0.13%.

Show 55 more citing papers

A precise determination of $\alpha$ using $B^0\to\rho^+\rho^-$ and $B^+\to K^{*0}\rho^+$
hep-ph 2006-04 accept novelty 7.0 of 10

An SU(3)-based analysis of B0 to rho+ rho- and B+ to K*0 rho+ data extracts the CKM angle alpha = 91 degrees with a few-degree theoretical uncertainty.
Charm Quark Contribution to K+ -> pi+ nu anti-nu at Next-to-Next-to-Leading Order
hep-ph 2006-03 conditional novelty 7.0 of 10

The paper presents the first complete NNLO QCD calculation of the charm quark contribution to K+ -> pi+ nu nu-bar, reducing the theoretical error in Pc(X) from 9.8% to 2.4%, with Pc(X)=0.38±0.04 and BR(K+ -> pi+ nu nu...
Bakamjian--Thomas construction and light-front zero modes in pseudoscalar transitions: A comparison with the covariant Bethe--Salpeter model
hep-ph 2026-10 accept novelty 6.0 of 10

Within the stated Bakamjian-Thomas light-front realization, the transverse and minus current extractions of f_minus agree, and the equality is proven analytically for a convergent rotationally invariant radial class.
Semileptonic $\bar{B}^*_{c} \to (P, V) \ell^- \bar{\nu}_{\ell}$ decays within the self-consistent light-front quark model
hep-ph 2026-09 conditional novelty 6.0 of 10

Semileptonic B*_c decays are predicted across many channels, with the Cabibbo-favored B*_s modes reaching branching fractions near 10^-6, but the absolute rates inherit a large uncertainty from a model-computed total width.
Revisiting two-body charmed anti-charmed baryonic $B$ decays
hep-ph 2026-09 conditional novelty 6.0 of 10

Including b to u anti-u q contributions in charmed baryonic B decays can explain data patterns and predict much larger rates for three specific decay modes.
The Very Nearly Right Theory of Flavor
hep-ph 2026-07 conditional novelty 6.0 of 10

A systematic scan of all nine-link Yukawa textures shows the quark CP phase clusters at pi/8, pi/4, pi/2, 3pi/8, and yields precise, falsifiable predictions for the CKM unitarity triangle angles.
A CKM blind spot: probing $b$-column rescaling with kaons
hep-ph 2026-07 accept novelty 6.0 of 10

A uniform rescaling of the CKM b-column is invisible to B-physics-only fits, and kaon data already bound it to −4%…+4% (2σ), with projections reaching ~2%.
$\bar{B}_{s,d}^{0} \to J/\psi \mu^{+}\mu^{-}$ Decays in QCD Factorization
hep-ph 2025-10 unverdicted novelty 6.0 of 10

Computes branching ratios of order 10^{-10} for Bs and 10^{-11} for Bd decays after NLO vertex corrections in QCD factorization, plus dimuon distributions and J/psi polarization.
Current-current operator contribution to the decay matrix in $B$-meson mixing at next-to-next-to-leading order of QCD
hep-ph 2025-05 conditional novelty 6.0 of 10

The full charm-mass dependence of the three-loop current-current contribution to the B-meson decay matrix is computed, yielding Delta_Gamma_s = (0.077 +/- 0.016) ps^-1 with the leading-term perturbative error reduced ...
Light scalars within the $\mathcal{CP}$-conserving Aligned-two-Higgs-doublet model
hep-ph 2024-12 conditional novelty 6.0 of 10

All seven light-scalar scenarios of the CP-conserving aligned two-Higgs-doublet model contain sizeable parameter regions compatible with current collider and flavour data, with the lightest new scalars bounded by LEP ...
KOTO vs. NA62 Dark Scalar Searches
hep-ph 2020-05 accept novelty 6.0 of 10

KOTO can search for KL to pi0 a to 4 photons at the 10^-9 level, and a strange-flavor-symmetric scalar model can violate the Grossman-Nir bound and accommodate the preliminary KOTO hint.
Beta decays as sensitive probes of lepton flavor universality
hep-ph 2020-02 accept novelty 6.0 of 10

Beta-decay data, reinterpreted through the muon-decay definition of the Fermi constant, tests lepton flavor universality in W-muon-neutrino couplings with a CKM enhancement of about twenty.
First measurement of the CKM angle $\phi_3$ with $B^{\pm}\to D(K_{\rm S}^0\pi^+\pi^-\pi^0)K^{\pm}$ decays
hep-ex 2019-08 accept novelty 6.0 of 10

First measurement of the CKM angle phi3 from B±->D(K_S0 pi+ pi- pi0)K± decays at Belle, giving phi3 = (5.7 +10.2 -8.8 ±3.5 ±5.7) degrees.
Long distance effects in inclusive rare $B$ decays and phenomenology of $\bar{B}\to X_d \ell^+\ell^-$
hep-ph 2019-08 conditional novelty 6.0 of 10

A new Standard Model prediction for the inclusive \bar B -> X_d \ell^+\ell^- decay that incorporates charmonium resonances, resolved power corrections, QED logarithms, and five-body contributions.
Neutral B-meson mixing from full lattice QCD at the physical point
hep-lat 2019-07 accept novelty 6.0 of 10

The first four-flavour lattice QCD determination of all five neutral-B mixing bag parameters gives |V_ts| = 0.04189(93), |V_td| = 0.00867(23), and Br(B_s to mu+mu-) = 3.81(18)e-9.
SU(3)-breaking ratios for $D_{(s)}$ and $B_{(s)}$ mesons
hep-lat 2018-12 conditional novelty 6.0 of 10

Domain-wall lattice QCD with two physical-pion-mass ensembles yields fDs/fD = 1.1740(51)(68), fBs/fB = 1.1949(60)(+95/-175), BBs/BBd = 0.9984(45)(+80/-63) and xi = 1.1939(67)(+95/-177).
Combined Explanations of the $b \to s \mu^+ \mu^-$ and $b \to c \tau^- {\bar\nu}$ Anomalies: a General Model Analysis
hep-ph 2018-06 accept novelty 6.0 of 10

Without any assumption about new-physics couplings, the S3 and U3 leptoquarks and the vector-boson triplet cannot jointly explain the two B anomalies, while the U1 leptoquark can, once lepton-flavour-violating constra...
New Physics in $b \rightarrow s \mu^+ \mu^-$: Distinguishing Models through CP-Violating Effects
hep-ph 2017-03 conditional novelty 6.0 of 10

CP-violating asymmetries in B to K(*) mu mu, especially A7 at low dilepton mass, can in principle separate leptoquark explanations of the b to s mu mu anomalies from Z-prime explanations and from each other.
Right-handed charged currents in the era of the Large Hadron Collider
hep-ph 2017-03 accept novelty 6.0 of 10

Low-energy precision data bound right-handed charged currents two to three orders of magnitude more tightly than the LHC, but WH angular distributions could identify them if a deviation appears.
Patterns of Flavour Violation in Models with Vector-Like Quarks
hep-ph 2016-09 accept novelty 6.0 of 10

A systematic survey of eleven vector-like-quark models shows their kaon and B-meson predictions fall into distinguishable patterns, and that combining mixing with rare-decay data fixes the new quark mass independently...
Constraining the top-Higgs sector of the Standard Model Effective Field Theory
hep-ph 2016-05 accept novelty 6.0 of 10

Electric dipole moment measurements bound CP-violating top-Higgs couplings about three orders of magnitude more tightly than collider searches, once one-loop mixing of the top operators into light-fermion dipoles is included.
Non-abelian gauge extensions for B-decay anomalies
hep-ph 2016-04 conditional novelty 6.0 of 10

Among minimal SU(2) x SU(2) x U(1) gauge extensions, only those where SU(2)_L is a diagonal subgroup and flavor non-universality comes from Yukawa couplings to vector-like fermions can address both B-decay anomalies, ...
$B^0_{(s)}$-mixing matrix elements from lattice QCD for the Standard Model and beyond
hep-lat 2016-02 accept novelty 6.0 of 10

Three-flavor lattice QCD yields the complete set of B-meson mixing matrix elements with full error budgets and correlations, giving the most precise xi to date and CKM elements that sit about 2 sigma from unitarity ex...
Phenomenology of semileptonic B-meson decays with form factors from lattice QCD
hep-ph 2015-10 accept novelty 6.0 of 10

With new lattice-QCD form factors, Standard Model predictions for B to pi/K mu mu run 1 to 2 sigma above LHCb measurements, and the same inputs give |Vtd| and |Vts| with uncertainties competitive with meson mixing.
Direct and indirect constraints on CP-violating Higgs-quark and Higgs-gluon interactions
hep-ph 2015-10 accept novelty 6.0 of 10

Combining EDM limits with LHC Run 1 data gives the current best bounds on CP-violating Higgs-quark and Higgs-gluon couplings, and hadronic/nuclear matrix element uncertainties dilute those bounds by up to orders of magnitude.
Family non-universal Z' models with protected flavor-changing interactions
hep-ph 2015-05 conditional novelty 6.0 of 10

Gauging the BGL flavor symmetry yields six anomaly-free Z-prime models with CKM-locked flavor-changing couplings and fixed lepton non-universality, three of which accommodate the LHCb R_K anomaly.
$B\to V\ell^+\ell^-$ in the Standard Model from Light-Cone Sum Rules
hep-ph 2015-03 accept novelty 6.0 of 10

Updated light-cone sum rule form factors for B to V l+ l- decays, with correlated uncertainties and combined lattice fits, sharpen Standard Model predictions for rare B decays and the extraction of |Vub|.
Inclusive B -> X_s l^+ l^-: Complete angular analysis and a thorough study of collinear photons
hep-ph 2015-03 accept novelty 6.0 of 10

Collinear photon emission reshapes the angular distribution of inclusive B -> X_s l+ l-; the authors compute those log-enhanced QED corrections, propose QED-only observables H3 and H4, and update Standard Model predic...
Addressing the LHC flavour anomalies with horizontal gauge symmetries
hep-ph 2015-03 conditional novelty 6.0 of 10

A single U(1)' horizontal gauge symmetry with charges (L_mu - L_tau) - a(B1 + B2 - 2B3) can simultaneously account for the B to K* mu mu, R(K), and h to mu tau anomalies, predicting tau to 3mu at a rate within reach o...
Reassessing the discovery potential of the $B \to K^{*} \ell^+\ell^-$ decays in the large-recoil region: SM challenges and BSM opportunities
hep-ph 2014-12 conditional novelty 6.0 of 10

Allowing power corrections to the heavy-quark limit to float reduces the B to K* mu mu angular anomaly from 3.7 sigma to below 2 sigma, and new muon-to-electron angular ratios are proposed as clean lepton-universality tests.
Present and Future K and B Meson Mixing Constraints on TeV Scale Left-Right Symmetry
hep-ph 2014-03 conditional novelty 6.0 of 10

With the previously neglected one-loop renormalization of the flavor-changing Higgs amplitude included, kaon and B mixing still permit a right-handed W boson near 3 TeV, and exclude hierarchical bidoublet vacuum expec...
B_l4 decays and the extraction of |V_ub|
hep-ph 2013-12 conditional novelty 6.0 of 10

An Omnès-type, model-independent representation of the B → ππℓν form factors is built, with B* pole terms supplying the left-hand cut, but the |V_ub| extraction itself is deferred to future fits to data.
Rare decay B -> K ll form factors from lattice QCD
hep-lat 2013-06 accept novelty 6.0 of 10

Unquenched lattice QCD with NRQCD bottom and HISQ light quarks yields the B to K scalar, vector and tensor form factors over the full q-squared range, with f0(0)=f+(0)=0.319(66) and fT(0)=0.270(95).
Standard Model predictions for B -> Kll with form factors from lattice QCD
hep-ph 2013-06 accept novelty 6.0 of 10

Unquenched lattice QCD form factors yield the Standard Model B to K lepton-pair branching fractions, the ratios R(mu/e) = 1.00023(63) and R(tau/l) = 1.159(40), and the angular flat term in experimental q-squared bins.
General Analysis of B -> K^(*) l^+ l^- Decays at Low Recoil
hep-ph 2012-12 accept novelty 6.0 of 10

At low hadronic recoil, the transversity observables H_T^(1,3,4,5) stay free of hadronic matrix elements even with the full dimension-six operator basis, and J_7 probes the operator product expansion at the few-percent level.
Probing Novel Scalar and Tensor Interactions from (Ultra)Cold Neutrons to the LHC
hep-ph 2011-10 accept novelty 6.0 of 10

Current bounds on scalar and tensor weak interactions come from nuclear 0+ to 0+ decays and radiative pion decay, and future neutron-decay and LHC measurements should compete once lattice QCD pins the nucleon scalar a...
New Physics in Gamma_12^s: (sbar b) (taubar tau) Operators
hep-ph 2011-09 conditional novelty 6.0 of 10

Operators coupling (sbar b) to (taubar tau) can enhance the Bs decay-matrix element Gamma_12^s by at most about 35 percent, too small to explain the Tevatron dimuon asymmetry.
The Impact of Flavour Changing Neutral Gauge Bosons on B->X_s gamma
hep-ph 2011-05 accept novelty 6.0 of 10

Two new contributions to B to X_s gamma from flavour-changing neutral gauge bosons are computed, including the first calculation of QCD mixing of neutral current-current operators into the dipole operator, yielding mo...
Continuum Limit of $B_K$ from 2+1 Flavor Domain Wall QCD
hep-lat 2010-12 accept novelty 6.0 of 10

Lattice QCD with 2+1 flavors of domain wall fermions at two lattice spacings yields the continuum-limit kaon bag parameter B_K-hat = 0.749(27), a 3.6 percent determination, using new non-exceptional RI-SMOM renormaliz...
Flavor Physics in the Randall-Sundrum Model: II. Tree-Level Weak-Interaction Processes
hep-ph 2009-12 accept novelty 6.0 of 10

In the minimal Randall-Sundrum model, tree-level Kaluza-Klein exchange makes Delta F=2 observables relatively model-independent while Delta F=1 rare decays depend strongly on right-handed top quark localization and th...
Rare K and B Decays in a Warped Extra Dimension with Custodial Protection
hep-ph 2008-12 conditional novelty 6.0 of 10

In a custodially protected Randall-Sundrum model, tree-level right-handed Z exchange can raise Br(K_L to pi0 nu nu-bar) by up to a factor of five while shifting rare B branching ratios by at most about 20 percent.
Seeking Sgluons
hep-ph 2008-10 conditional novelty 6.0 of 10

Sgluon pair production followed by decays into like-sign tops is the most promising LHC search channel for the color-octet scalar of R-symmetric supersymmetry, with an estimated reach near 1 TeV.
Flavor Physics in the Randall-Sundrum Model: I. Theoretical Setup and Electroweak Precision Tests
hep-ph 2008-07 conditional novelty 6.0 of 10

Exact Kaluza-Klein solutions for bulk gauge and fermion fields in the Randall-Sundrum model yield the full set of tree-level flavor-changing couplings, and show the minimal model survives electroweak precision data fo...
Electroweak Corrections to the Charm Quark Contribution to K+ -> pi+ nu nu-bar
hep-ph 2008-05 accept novelty 6.0 of 10

Adding QED and electroweak corrections to the charm contribution of K+ -> pi+ nu nu-bar shifts P_c(X) up by about 2% to 0.372 +/- 0.015 and yields a branching ratio of (8.5 +/- 0.7) x 10^-11.
SuperB: A High-Luminosity Asymmetric e+ e- Super Flavor Factory. Conceptual Design Report
hep-ex 2007-09 conditional novelty 6.0 of 10

A design study argues that a low-emittance, ILC-derived asymmetric e+e- ring with a crabbed-waist final focus can deliver 10^36 cm^-2 s^-1 luminosity at B-Factory-scale power, enabling percent-level flavour-physics tests.
Theoretical update of Bs-Bs-bar mixing
hep-ph 2006-12 accept novelty 6.0 of 10

A new operator basis shrinks the theoretical uncertainty in the Bs width difference, and applying it to DØ data yields a roughly 2σ hint of physics beyond the Standard Model in Bs mixing.
NNLO QCD corrections to the B -> X_s gamma matrix elements using interpolation in m_c
hep-ph 2006-09 conditional novelty 6.0 of 10

A three-loop QCD matrix element for B -> X_s gamma is computed in the heavy-charm limit and interpolated to the physical charm mass, giving a Standard Model branching ratio of (3.15 +/- 0.23) x 10^-4 above 1.6 GeV.
The Unitarity Triangle Fit in the Standard Model and Hadronic Parameters from Lattice QCD: A Reappraisal after the Measurements of Delta m_s and BR(B to tau nu)
hep-ph 2006-06 accept novelty 6.0 of 10

Adding the CDF Delta m_s and Belle B to tau nu measurements to the global CKM fit yields data-driven values of the kaon B-parameter and the B mixing and decay constants, in broad agreement with lattice QCD, and expose...
Separation of unistochastic matrices from the double stochastic ones. Recovery of a 3 x 3 unitary matrix from experimental data
math-ph 2006-03 conditional novelty 6.0 of 10

For 3x3 doubly stochastic matrices, the paper gives a constructive necessary and sufficient condition: the matrix is unistochastic exactly when a derived CP-phase cosine lies in [-1,1], and the unitary matrix is then ...
Unquenched determination of the kaon parameter B_K from improved staggered fermions
hep-lat 2006-03 conditional novelty 6.0 of 10

A first unquenched lattice QCD computation of B_K with improved staggered fermions gives \hat B_K = 0.83 ± 0.18, dominated by perturbative matching uncertainty.
Constraints on B and Higgs Physics in Minimal Low Energy Supersymmetric Models
hep-ph 2006-03 accept novelty 6.0 of 10

The Tevatron bound on B_s -> mu+ mu- strongly limits non-standard Higgs and B_s mixing effects in minimal flavor violating supersymmetry, and the paper corrects the double-penguin formulas for the kaon sector.
Hunting the CKM weak phase with time-integrated Dalitz analyses of Bs -> K pi pi decays
hep-ph 2006-02 conditional novelty 6.0 of 10

A ratio of isospin-related Bs to K pi pi amplitudes is shown to equal exp(-2i gamma), yielding a clean extraction of the CKM weak phase gamma.
Electromagnetic Logarithms in B -> X_s l+ l-
hep-ph 2005-12 accept novelty 6.0 of 10

Including the collinear QED logarithm ln(m_b^2/m_l^2) in the four-fermion matrix elements shifts the low-q^2 B -> X_s mu+ mu- branching ratio to (1.59 ± 0.11) x 10^-6, completing the logarithmically enhanced electroma...
Final State Interactions in Hadronic B Decays
hep-ph 2004-09 conditional novelty 6.0 of 10

Long-distance rescattering among two-body hadronic intermediate states can substantially enhance color-suppressed B decay modes and reverse the sign of direct CP asymmetries relative to short-distance predictions.
Flavor Structure of Warped Extra Dimension Models
hep-ph 2004-08 conditional novelty 6.0 of 10

With anarchic five-dimensional Yukawas and Kaluza-Klein masses near 3 TeV, warped extra dimension models predict a neutron electric dipole moment roughly twenty times the current bound, alongside order-one new physics...

See all 152 Pith citations

How later papers used it

316 later papers cite it

Evidence: substantial. 306 of the citing papers share no author with it, and 194 of those carry a confident label from Pith's citation classifier.

Pith read 40 of the 481 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

29 later papers by other authors are listed below: 2 used its method or tool, 26 used its data or values and 1 compared its own results with it. 1 more paper by the same authors is listed: 1 used its method or tool.

Uses its method or tool 3 of 23 papers with this label · 1 by the same authors

Performed a combined analysis of branching ratios in the 2HDM Type II within the frequentist statistical scheme developed by the CKMfitter group.

The Two Higgs Doublet of Type II facing flavour physics data (2009) · 1.00 · paraphrased: the licence does not allow quoting
Established a procedure involving a global chi-squared fit based on the CKMfitter package to generate pseudoexperiments and fit samples of events.

Study of CKM angle $\gamma$ sensitivity using flavor untagged $B^0_s\rightarrow \tilde{D}^{(*)0}\phi$ decays (2020) · 1.00 · paraphrased: the licence does not allow quoting

By the same authors

With these results for $R_±$ and $𝒜_±$, we constrain the angle $ϕ_3$ using a frequentist approach as implemented in the CkmFitter package [ref] .

Measurement of branching-fraction ratios and $CP$ asymmetries in $B^{\pm} \to D_{CP\pm}K^{\pm}$ decays at Belle and Belle II (2023) (same authors) · Results · 1.00

Uses its data or values 26 of 157 papers with this label

Took the values in its table from the CKMfitter group's web update of this paper, among other sources.

One constraint to kill them all? (2017) · 1.00 · paraphrased: the licence does not allow quoting
Presented an update of SM predictions for Delta Gamma, Delta M and a_sl in the B_s^0 and B_d^0 systems using the latest CKM parameters from CKMfitter.

On the ultimate precision of meson mixing observables (2016) · 1.00 · paraphrased: the licence does not allow quoting
We take the Wilson coefficients from Ref. [ref] , the CKM elements from Ref. [ref] , the meson masses and lifetimes from Ref. [ref] , and the $b$- and $c$-quark masses from Ref. [ref] .

$B\to\pi\ell\ell$ form factors for new-physics searches from lattice QCD (2015) · Introduction · 1.00
Used the updated global fit results from the CKMfitter group for the CKM matrix elements and CKM angles.

Charmless Two-body $B(B_s)\to VP$ decays In Soft-Collinear-Effective-Theory (2008) · 1.00 · paraphrased: the licence does not allow quoting
Fixed the relevant CKM elements to their best-fit values from this paper in the SM contributions.

$K\to \pi \nu\overline{\nu}$ in the MSSM in Light of the $\epsilon^{\prime}_K/\epsilon_K$ Anomaly (2017) · 1.00 · paraphrased: the licence does not allow quoting
In our numerical analysis, apart from already discussed form factors and the Wilson coefficients, we use results of CKMfitter Group [ref] for values of CKM elements, while particle masses and their lifetime values are taken from Particle Data Group [ref] .

$\Lambda_b\rightarrow \Lambda(\to p \pi^-) \ell^+\ell^-$ as probe of CP-violating New Physics (2022) · CP-Violating Asymmetries and Results · 1.00
Took the CKM matrix elements from this paper.

Studying Exclusive Semi-leptonic $b\to (s,d) \nu \bar{\nu}$ Decays in the MSSM without R-parity (2009) · 1.00 · paraphrased: the licence does not allow quoting
Used |V_tb V_ts^*| = 0.0405(8) from this paper.

Standard Model predictions for B -> Kll with form factors from lattice QCD (2013) · 1.00 · paraphrased: the licence does not allow quoting
Took the CKM parameters from CKMfitter.

Bd \to \pi^- K^{(*)+} and Bs \to \pi^+(\rho^+) K^- decays with QCD factorization and flavor symmetry (2010) · 1.00 · paraphrased: the licence does not allow quoting
Used V^*_tb V_ts = 0.0405 from this paper in its numerical analysis.

New Physics Contribution to $B_s \to \mu^+ \mu^-$ within R-Parity Violating Supersymmetric Models (2013) · 1.00 · paraphrased: the licence does not allow quoting
Assumed the SM with this paper to obtain its result.

Decoding (Pseudo)-Scalar Operators in Leptonic and Semileptonic $B$ Decays (2018) · 1.00 · paraphrased: the licence does not allow quoting
As for the CKM matrix elements, we use the standard parametrisation, taking the values of $|V_us|$, $|V_cb|$, $|V_ub/V_cb|$, and $δ$, from the CKMfitter [ref] (similar values can be obtained from the UTFit [ref] ).

Two body non-leptonic $D^0$ decays from LCSR and implications for $\Delta a^{\rm dir}_{\rm CP}$ (2023) · Numerical analysis and results · 1.00
Took a range for gamma of (68 ± 4) degrees from this paper.

Calculating Phases Between B => K* pi Amplitudes (2010) · 1.00 · paraphrased: the licence does not allow quoting
Used the same value for |V_tb V_ts^*| = 0.0405(8) from this paper.

Form factors for the processes $B_c^+ \to D^0 \ell^+ \nu_{\ell}$ and $B_c^+ \to D_s^+ \ell^+ \ell^- (\nu \overline{\nu})$ from lattice QCD (2021) · 1.00 · paraphrased: the licence does not allow quoting
Took |V_tb| = 0.99912 from CKM unitarity in this paper to infer values for |V_td| and |V_ts|.

$B^0_{(s)}$-mixing matrix elements from lattice QCD for the Standard Model and beyond (2016) · 0.98 · paraphrased: the licence does not allow quoting
Used CKM elements from the CKMfitter group's web update of this paper to predict the mass difference of the neutral mesons.

CP Violation in the $B_s^0$ system (2015) · 0.91 · paraphrased: the licence does not allow quoting
Took into account all indirect constraints from the global unitarity-triangle fit to obtain its SM prediction for |epsilon_K|.

Little Randall-Sundrum models: epsilon_K strikes again (2008) · 0.89 · paraphrased: the licence does not allow quoting
Took into account all indirect constraints from the global unitarity-triangle fit to obtain its SM prediction for |epsilon_K|.

Flavor Physics in the Randall-Sundrum Model: II. Tree-Level Weak-Interaction Processes (2009) · 0.93 · paraphrased: the licence does not allow quoting
Took |V_tb| = 0.9991 from CKM unitarity in this paper to infer values for |V_td| and |V_ts|.

Phenomenology of semileptonic B-meson decays with form factors from lattice QCD (2015) · 0.98 · paraphrased: the licence does not allow quoting
Used CKM fits to find A_s ell.

Second order direct CP asymmetry in B_(s) -> X l nu (2010) · 0.98 · paraphrased: the licence does not allow quoting
Computed the quark-mixing parameters from the ICHEP 2016 update by the CKMFitter Group.

A minimal non-supersymmetric SO(10) model with Peccei--Quinn symmetry (2018) · 0.99 · paraphrased: the licence does not allow quoting
We start from the current determination of $α$ performed by the CKMfitter group [ref] .

Prospects for $B^0_{(s)}\to\pi^0\pi^0$ and $B^0_{(s)}\to\eta\eta$ modes and corresponding $CP$ asymmetries at Tera-$Z$ (2022) · Extraction of the CKM angle $α$ and the global fit · 0.91
The black line stands for the unitarity condition: $|V_ud|^2+|V_us|^2 + |V_ub|^2=1$ with $|V_ub| ≈0.00377$ [ref] .

Theoretical point of view on Cabibbo angle anomaly (2024) · Current status of Cabibbo angle anomaly · 0.86
Our inputs are the Bag parameters given in [ref] and the values for $|V_us|, |V_cb|, |V_ub|,γ$ from the CKMfitter's Spring `21 update [ref] .

Enhancing $B_s \to e^+ e^-$ to an Observable Level in the Two-Higgs-Doublet Model (2022) · Enhancing $B_s →e^+ e^-$ and Phenomenological Constraints · 0.93
Took the Wolfenstein parameters to show a contour plot of B(B_s to pi+ pi-).

Implications of the recent measurement of pure annihilation $B_s \to \pi^+ \pi^-$ decays in QCD factorization (2011) · 0.99 · paraphrased: the licence does not allow quoting
Took input parameters from this paper to draw its figure.

Flavor dependence of annihilation parameters in QCD factorization (2013) · 0.92 · paraphrased: the licence does not allow quoting

Compares with it 1 of 37 papers with this label

Compared its own resulting CKM matrix with experimental values at m_Z, finding agreement within 3 sigma.

A Viable Randall-Sundrum Model for Quarks and Leptons with T' Family Symmetry (2009) · 0.95 · paraphrased: the licence does not allow quoting

How the literature uses it

284 arXiv papers cite this in 428 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 167 sentences without a confident label

Uses its method or tool 17 papers

A combined analysis of their branching ratios in the light of the 2HDM Type II is then performed within the frequentist statistical scheme developed by the CKMfitter group [ref] .

The Two Higgs Doublet of Type II facing flavour physics data · Introduction · 1.00
The input values and statistical procedure of this fit can be found in Ref. [ref] .

CKM Substructure · Fits of the CKM matrix elements · 0.88
The CKMfitter group aims at this goal by combining a large set of constraints from flavour physics, using a standard $χ^2$-like frequentist approach, in addition to a specific (Rfit) scheme to treat theoretical uncertainties [ref] (see refs.

Current status of the Standard Model CKM fit and constraints on $\Delta F=2$ New Physics · Introduction · 0.93

Uses its data or values 141 papers

The values in Table [ref] are taken from the PDG [ref] , from non-relativistic sum rules (NRSR) [ref] , from the CKMfitter group (web-update of [ref] – similar values can be taken from the UTfit group [ref] ) and the non-perturbative parameters from FLAG (web-update of [ref] ).

One constraint to kill them all? · Numerical input for theory predictions · 1.00
Based on these criteria, and the central values of the CKM elements from CKMfitter [ref] , we found exactly two independent relations, which are given by Eq. ([ref]).

CKM Substructure · Fits of the CKM matrix elements · 0.99
Using CKM fits [ref] , Im(V_tb^⋆V_ts V_cb V_cs^⋆)/|V_cb |^2 ≈Arg(V_tb^⋆V_ts V_cb V_cs^⋆) ≡-β_s = -0.018 , we then find A_s ℓ = (-3.2 ±0.9) ×10^-9 .

Second order direct CP asymmetry in B_(s) -> X l nu · Direct asymmetry in the CKM framework · 0.98

Compares with it 29 papers

The resulting CKM matrix from these input parameters is given by [equation] The absolute values of the CKM matrix elements agree with experimental values at $m_Z$ within $3σ$ [ref] : [equation] In addition, we have a predictions for $CP$ violation in the quark and lepton sectors.

A Viable Randall-Sundrum Model for Quarks and Leptons with T' Family Symmetry · Results · 0.95
Focusing just on the extraction of the CKM element, we obtain [equation] These values are in good agreement with the world averages [ref] , with the largest tension slightly exceeding $1 σ$ for $|V_ub|$.

Form factors and phenomenology of $\boldsymbol{B_{(s)}}$ and $\boldsymbol{D_{(s)}}$ semileptonic decays to $\boldsymbol{\eta}$ and $\boldsymbol{\eta^\prime}$ · CKM matrix elements extractions · 0.99
The results are [equation] and agree well with the Belle result $γ=(53±20)^∘$ obtained from tree-level processes, and results from global fits [ref] .

Meson distribution amplitudes - applications to weak radiative B decays and B transition form factors · Extraction Of CKM Parameters · 0.96

Cites it as background 29 papers

The values of top quark related CKM matrix elements, $$, $$ and $$, are extracted indirectly through the contribution of the top quark in B-$B̅$ oscillations or loop-mediated rare K and B meson decays [ref] .

Model-independent constraints on the CKM matrix elements $|V_{tb}|$, $|V_{ts}|$ and $|V_{td}|$ · Introduction · 0.95
A rich variety of observables is used to probe the structure of the CKM matrix [ref] , including processes dominated by SM tree-level contributions, processes for which in the SM there is no tree-level contribution, processes that individually rule out a vanishing CP violating phase, or yet processes that are individually compatible with the absence of CP violation.

2023 update of the extraction of the CKM matrix elements · Introduction · 0.87
In the case of three generations of quarks, the physical content of this matrix reduces to four real parameters, among which one phase, the only source of $CP$ violation in the SM (neglecting $CP$-violating effects induced by the strong-interaction $θ$-term or neutrino masses): [equation] One can exploit the unitarity of the CKM matrix to determine all its elements (and when needed, to obtain their Wolfenstein expansion in powers of $λ$) [ref] .

Current status of the Standard Model CKM fit and constraints on $\Delta F=2$ New Physics · Introduction · 0.95

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

[1] [6]

A. H¨ ocker, H. Lacker, S. Laplace and F. Le Diberder, Eur. Phys. J. C21, 225 (2001)

View on Pith 2001

[2] [1]

N. Cabibbo, Phys. Rev. Lett. 10, 351 (1963)

View on Pith 1963

[3] [2]

M. Kobayashi and T. Maskawa, Prog. Theor. Phys. 49, 652 (1973)

View on Pith 1973

[4] [3]

L. Wolfenstein, Phys. Rev. Lett. 51, 1945 (1983)

View on Pith 1983

[5] [4]

A.J. Buras, M.E. Lautenbacher and G. Ostermaier, Phys. R ev. D50, 3433 (1994)

View on Pith 1994

[6] [5]

I.Y. Bigi, V.A. Khoze, N.G. Uraltsev and A.I. Sanda, in “CP Violation ”, C. Jarlskog Ed., World Scientiﬁc, Singapore (1988)

View on Pith 1988

[7] [7]

Partially updated plots and results are available at the CKMﬁtter web site: http://ckmﬁtter.in2p3.fr and its mirror http://www.slac .stanford.edu/xorg/ckmﬁtter

View on Pith

[8] [8]

M. Ciuchini, G. D’Agostini, E. Franco, V. Lubicz, G. Mart inelli, F. Parodi, P. Roudeau and A. Stocchi, J. High Energy Phys. 0107, 013 (2001)

View on Pith 2001

[9] [9]

M. Battaglia et al. , CERN-2003-002, Cern Yellow Report, Based on the Workshop o n CKM Unitarity Triangle (CERN 2002-2003), Geneva, Switzerl and, 13-16 Feb 2002, hep- ph/0304132

View on Pith 2003

[10] [10]

A.J. Buras, F. Parodi and A. Stocchi, J. High Energy Phys ., 0301, 029 (2003); A. Ali, Lectures given at the International Meeting on Fundamental Physics, Soto de Cangas, Spain, 23-28 Feb. 2003, hep-ph/0312303; G. Eigen, G.P. Dubo is-Felsmann, D.G. Hitlin and F.C. Porter, Contributed to International Europhysics Conference on High-Energy Physics (HEP 2003...

View on Pith Pith review arXiv 2003

[11] [11]

L.L. Chau and W.Y. Keung, Phys. Rev. Lett. 53, 1802 (1984)

View on Pith 1984

[12] [12]

Particle Data Group (K. Hagiwara et al.), Phys. Rev. D66, 010001 (2002 and 2003 update)

View on Pith 2002

[13] [13]

C. Jarlskog, Phys. Rev. Lett. 55, 1039 (1985)

View on Pith 1985

[14] [14]

G.C. Branco, L. Lavoura and J.P. Silva, CP Violation , The Intern. Series of Monographs on Physics - 103, Oxford Science Publications, Oxford, UK (1 999)

View on Pith

[15] [15]

E787 Collaboration (S. Adler et al. ), Phys. Rev. Lett. 88, 041803 (2002)

View on Pith 2002

[16] [16]

E949 Collaboration (A.V. Artamonov et al. ), hep-ex/0403036 (2004), http://www.phy.bnl.gov/e949

View on Pith Pith review arXiv 2004

[17] [17]

I.S. Towner and J.C. Hardy, J. Phys. G: Nucl. Part. Phys. 29, 197 (2003)

View on Pith 2003

[18] [18]

K. Saito and A.W. Thomas, Phys. Lett. B363, 157 (1995)

View on Pith 1995

[19] [19]

H. Abele et al. , Phys. Rev. Lett. 88, 211801 (2002)

View on Pith 2002

[20] [20]

D. Pocanic (for the PIBETA Collaboration), Talk given a t 2nd Workshop on the CKM Unitarity Triangle, Durham, England, 5-9 Apr 2003, eConf C0304052, WG606 References 167

View on Pith 2003

[21] [21]

J.F. Donoghue, B.R. Holstein and S.W. Klimt, Phys. Rev. D35, 934 (1987)

View on Pith 1987

[22] [22]

R. Flores-Mendieta, A. Garcia and G. Sanchez-Colon, Ph ys. Rev. D54, 6855 (1996)

View on Pith 1996

[23] [23]

N. Cabibbo, E. C. Swallow and R. Winston, APS-123-QED, h ep-ph/0307214 (2003)

View on Pith 2003

[24] [24]

H. Leutwyler and M. Roos, Z. Phys. C25, 91 (1984)

View on Pith 1984

[25] [25]

E.A. Paschos and U. T¨ urke, Phys. Rep. 178, 145 (1989)

View on Pith 1989

[26] [26]

W. Jaus, Phys. Rev. D44, 2851 (1991)

View on Pith 1991

[27] [27]

P. Post, K. Schilcher, Eur. Phys. J. C25, 427 (2002)

View on Pith 2002

[28] [28]

J. Bijnens and P. Talavera, Nucl. Phys. B 669 , 341 (2003)

View on Pith 2003

[29] [29]

V. Cirigliano, H. Neufeld and H. Pichl, hep-ph/0401173

View on Pith Pith review arXiv

[30] [30]

D. Becirevic et al. , hep-ph/0403217

View on Pith Pith review arXiv

[31] [31]

W.J. Marciano and A. Sirlin, Phys. Rev. Lett. 56, 22 (1986)

View on Pith 1986

[32] [32]

H.H. Williams et al. , Phys. Rev. Lett. 33, 240 (1974); T. Becherrawy et al. , Phys. Rev. D1, 1452 (1970)

View on Pith 1974

[33] [33]

V. Cirigliano, Talk given at 38th Rencontres de Moriond on Electroweak Interactions and Uniﬁed Theories, Les Arcs, France, 15-22 Mar 2003, hep-ph/0 305154

View on Pith 2003

[34] [34]

BNL-E865 Collaboration (A. Sher et al. ), AIP Conf. Proc. 698, 381 (2004), hep- ex/0305042

View on Pith 2004

[35] [35]

B. Sciascia (for the KLOE Collaboration), Talk given at 2nd Workshop on the CKM Unitarity Triangle, Durham, England, 5-9 Apr 2003, eConf C0304052, WG607

View on Pith 2003

[36] [36]

S. Miscetti (for the KLOE Collaboration), Talk given at 39th Rencontres de Moriond: Electroweak Interactions and Uniﬁed Theories La Thuile, Va l d’Aoste, Italy, Mar 21-28 2004, hep-ex/0405040

View on Pith Pith review arXiv 2004

[37] [37]

KTeV Collaboration, (T. Alexopoulos et al. ), hep-ex/0406001

View on Pith Pith review arXiv

[38] [38]

E. Gamiz, M. Jamin, A. Pich, J. Prades and F. Schwab, J. Hi gh Energy Phys. 0301, 060 (2003)

View on Pith 2003

[39] [39]

CDHS Collaboration (H. Abramowicz et al. ), Z. Phys. C15, 19 (1982)

View on Pith 1982

[40] [40]

CCFR Collaboration (A.O. Bazarko et al. ), Z. Phys. C65, 189 (1995)

View on Pith 1995

[41] [41]

CHARM II Collaboration (P. Vilain et al. ), Eur. Phys. J. C11, 19 (1999)

View on Pith 1999

[42] [42]

T. Bolton, KSU-HEP-97-04, hep-ex/9708014 (1997)

View on Pith Pith review arXiv 1997

[43] [43]

FNAL-E531 Collaboration (N. Ushida et al. ), Phys. Lett. B206, 375 (1988)

View on Pith 1988

[44] [44]

CLEO Collaboration (Y. Kubota et al. ), Phys. Rev. D54, 2994 (1996)

View on Pith 1996

[45] [45]

M. Bargiotti et al. , Riv. Nuovo Cim. 23 N3, 1 (2000)

View on Pith 2000

[46] [46]

L. Montanet et al. , Phys. Rev. D50, 1173 (1994) 168 References

View on Pith 1994

[47] [47]

ALEPH Collaboration (R. Barate et al. ), Phys. Lett. B453, 107 (1999); ALEPH Collabo- ration (R. Barate et al. ), ALEPH 99-064 CONF-99-038; ALEPH Collaboration (R. Barat e et al. ), Phys. Lett. B465, 349 (1999)

View on Pith 1999

[48] [48]

DELPHI Collaboration (P. Abreu et al. ), Phys. Lett. B439, 209 (1998)

View on Pith 1998

[49] [49]

OPAL Collaboration (G. Abbiendi et al. ), Phys. Lett. B490, 71 (2000)

View on Pith 2000

[50] [50]

LEP Electroweak Working Group, CERN-EP-2001-098, hep -ex/0112021 (2001)

View on Pith 2001

[51] [51]

K. Benslama (for the CLEO-c Collaboration), Talk given at 37th Rencontres de Moriond on Electroweak Interactions and Uniﬁed Theories, Les Arcs, France, 9-16 Mar 2002, hep- ex/0205003

View on Pith 2002

[52] [52]

N. Isgur and M. Wise, Phys. Lett. B232, 113 (1989); Phys. Lett. 237, 527 (1990)

View on Pith 1989

[53] [53]

H. Georgi, Phys. Lett. B238, 395 (1990)

View on Pith 1990

[54] [54]

M. Luke, Phys. Lett. B252, 447 (1990)

View on Pith 1990

[55] [55]

N. Uraltsev, Talk given at Flavor Physics and CP Violation (FPCP 2003), Paris, France, 3-6 Jun 2003, hep-ph/0309081

View on Pith Pith review arXiv 2003

[56] [56]

M. Shifman, N. Uraltsev and A. Vainshtein, Phys. Rev. D51, 2217 (1995); Erratum-ibid. D52, 3149 (1995)

View on Pith 1995

[57] [57]

M. Neubert, Phys. Lett. B338, 84 (1994)

View on Pith 1994

[58] [58]

A. Falk and M. Neubert, Phys. Rev. D47, 2965 (1993)

View on Pith 1993

[59] [59]

A. Kronfeld, Phys. Rev. D62, 014505 (2000)

View on Pith 2000

[60] [60]

J. Harada et al. , Phys. Rev. D65, 094514 (2002)

View on Pith 2002

[61] [61]

S. Hashimoto et al. , Phys. Rev. D66, 014503 (2002)

View on Pith 2002

[62] [62]

The Heavy Flavor Averaging Group, http://www.slac.st anford.edu/xorg/hfag/ (Summer 2003 and Winter 2004 averages)

View on Pith 2003

[63] [63]

I.I. Bigi, M. Shifman and N.G. Uraltsev, Annu. Rev. Nucl . Part. Sci. 47, 591 (1997)

View on Pith 1997

[64] [64]

I.I. Bigi, M. Shifman, N. Uraltsev and A. Vainshtein, Ph ys. Rev. D56, 4017 (1997); Phys. Rev. D52, 196 (1995)

View on Pith 1997

[65] [65]

CLEO Collaboration (S. Chen et al. ), Phys. Rev. Lett. 87, 251807 (2001)

View on Pith 2001

[66] [66]

C.W. Bauer, Z. Ligeti, M. Luke, A.V. Manohar and M. Trott , Phys. Rev. D70, 094017 (2004)

View on Pith 2004

[67] [67]

K. Schubert, Talk given at 21st International Symposiu m on Lepton and Photon Interac- tions at High Energies (LP 03), Batavia, Illinois, 11-16 Aug 2003

View on Pith 2003

[68] [68]

BABA RCollaboration (B. Aubert et al. ), BABA R-PUB-03-045, hep-ex/0403030

View on Pith Pith review arXiv

[69] [69]

BABA RCollaboration (B. Aubert et al. ), BABA R-CONF-03-034, hep-ex/0403031

View on Pith Pith review arXiv

[70] [70]

BABA RCollaboration (B. Aubert et al. ), BABA R-PUB-04-007, hep-ex/0404017 References 169

View on Pith Pith review arXiv

[71] [71]

BABA RCollaboration (B. Aubert et al. ), Phys. Rev. Lett. 90, 181801 (2003)

View on Pith 2003

[72] [72]

CLEO Collaboration (S.B. Athar et al. ), Phys. Rev. D68, 072003 (2003)

View on Pith 2003

[73] [73]

ARGUS Collaboration (H. Albrecht et al. ), Phys. Lett. B255, 297 (1991)

View on Pith 1991

[74] [74]

CLEO Collaboration (R. Fulton et al. ), Phys. Rev. Lett. 64, 16 (1990)

View on Pith 1990

[75] [75]

CLEO Collaboration (J. Bartelt et al. ), Phys. Rev. Lett. 71, 4111 (1993)

View on Pith 1993

[76] [76]

G. Altarelli, N. Cabibbo, G. Corb` o, L. Maiani and G. Mar tinelli, Nucl. Phys. B208, 365 (1982)

View on Pith 1982

[77] [77]

N. Isgur, D. Scora, B. Grinstein and M.B. Wise, Phys. Rev . D39, 799 (1989)

View on Pith 1989

[78] [78]

J.G. K¨ orner and G.A. Schuler, Z. Phys. C38, 511 (1988); Erratum-ibid. C41, 690 (1989)

View on Pith 1988

[79] [79]

M. Wirbel, B. Stech and M. Bauer, Z. Phys. C29, 637 (1985)

View on Pith 1985

[80] [80]

CLEO Collaboration (A. Bornheim et al. ), Phys. Rev. Lett. 88, 231803 (2002)

View on Pith 2002

[81] [81]

BABA RCollaboration (B. Aubert et al. ), BABAR-CONF-02-012, Contributed to 31st In- ternational Conference on High Energy Physics (ICHEP 2002) , Amsterdam, The Nether- lands, 24-31 Jul 2002, hep-ex/0207081

View on Pith Pith review arXiv 2002

[82] [82]

Belle Collaboration (K. Abe et al. ), BELLE-CONF-0325 (2003), Contributed to Interna- tional Europhysics Conference on High-Energy Physics (HEP 2001), Budapest, Hungary, 12-18 Jul 2001

View on Pith 2003

[83] [83]

A.K. Leibovich, Z. Ligeti and M.B. Wise, Phys. Lett. B539, 242 (2002)

View on Pith 2002

[84] [84]

C.W. Bauer, M. Luke and T. Mannel, Phys. Lett. B543, 261 (2002)

View on Pith 2002

[85] [85]

M. Neubert, Phys. Lett. B543, 269 (2002)

View on Pith 2002

[86] [86]

C.N. Burrell, M.E. Luke and A.R. Williamson, Phys.Rev. D69, 074015 (2004)

View on Pith 2004

[87] [87]

I.I.Y. Bigi and N. Uraltsev, Int. J. Mod. Phys. A16, 5201 (2001)

View on Pith 2001

[88] [88]

M.B. Voloshin, Phys. Lett. B515, 74 (2001)

View on Pith 2001

[89] [89]

DELPHI Collaboration (P. Abreu et al. ), Phys. Lett. B478, 14 (2000)

View on Pith 2000

[90] [90]

BABA RCollaboration (B. Aubert et al. ), Phys. Rev. Lett. 92, 071802 (2004)

View on Pith 2004

[91] [91]

CLEO Collaboration (A. Bornheim et al.), CLEO-CONF-02-08, Contributed to 31st Inter- national Conference on High Energy Physics (ICHEP 2002), Am sterdam, The Netherlands, 24-31 Jul 2002, hep-ex/0207064

View on Pith Pith review arXiv 2002

[92] [92]

A. Sugiyama (for the Belle Collaboration), Talk given a t 38th Rencontres de Moriond on Electroweak Interactions and Uniﬁed Theories, Les Arcs, Fr ance, 15-22 Mar 2003, hep- ex/0306020

View on Pith 2003

[93] [93]

ALEPH collaboration (R. Barate et al. ), Eur. Phys. J. C6, 555 (1999)

View on Pith 1999

[94] [94]

OPAL collaboration, (G. Abbiendi et al. ), Eur. Phys. J. C21, 399 (2001) 170 References

View on Pith 2001

[95] [95]

L. Gibbons (for the CLEO Collaboration), To appear in th e proceedings of 9th Interna- tional Conference on B Physics at Hadron Machines (Beauty 2003), Pittsburgh, Penn syl- vania, 14-18 Oct 2003, hep-ex/0402009

View on Pith Pith review arXiv 2003

[96] [96]

O. Cat` a and S. Peris, hep-ph/0406094

View on Pith Pith review arXiv

[97] [97]

T. Trippe, private communication (2004)

View on Pith 2004

[98] [98]

KTeV Collaboration, (T. Alexopoulos et al. ), hep-ex/0406002

View on Pith Pith review arXiv

[99] [99]

L. Lellouch, Nucl. Phys. Proc. Suppl. 94, 142 (2001)

View on Pith 2001

[100] [100]

J. Bijnens and J. Prades, Nucl. Phys. B444, 523 (1995); J. High Energy Physics 01, 002 (2000); S. Peris and E. de Rafael, Phys. Rev. Lett. 490, 213 (2000)

View on Pith 1995

[101] [101]

G. Buchalla, A.J. Buras and M.E. Lautenbacher, Rev. Mo d. Phys. 68, 1125 (1996)

View on Pith 1996

[102] [102]

T. Inami and C.S. Lim, Prog. Theor. Phys. 65, 297 (1981); Erratum-ibid. 65, 1772 (1981)

View on Pith 1981

[103] [103]

L. Cerrito (for the CDF and D0 Collaboration), To appea r in the proceedings of 39th Rencontres de Moriond on QCD and High-Energy Hadronic Inter actions, La Thuile, Italy, 28 Mar - 4 Apr 2004, hep-ex/0405046

View on Pith Pith review arXiv 2004

[104] [104]

K. Melnikov, T. van Ritbergen, Phys. Lett. B482, 99 (2000)

View on Pith 2000

[105] [105]

N. Gray, D.J. Broadhurst, W. Grafe and K. Schilcher, Z. Phys. C48, 673 (1990)

View on Pith 1990

[106] [106]

D.J. Broadhurst, N. Gray and K. Schilcher, Z. Phys. C52, 111 (1991)

View on Pith 1991

[107] [107]

S. Herrlich and U. Nierste, Nucl. Phys. B419, 292 (1994)

View on Pith 1994

[108] [108]

U. Nierste, Ref. [ 9] and private communication (2003)

View on Pith 2003

[109] [109]

D. Becirevic, Talk given at 2nd Workshop on the CKM Unit arity Triangle, Durham, England, 5-9 Apr 2003, hep-ph/0310072

View on Pith Pith review arXiv 2003

[110] [110]

M.J. Booth, Phys. Rev. D51, 2338 (1995)

View on Pith 1995

[111] [111]

S.R. Sharpe and Y. Zhang, Phys. Rev. D53, 5125 (1996)

View on Pith 1996

[112] [112]

C. Bernard, T. Blum and A. Soni, Phys. Rev. D58 014501 (1998)

View on Pith 1998

[113] [113]

JLQCD Collaboration (N. Yamada et al. ), Nucl. Phys. B Proc. Suppl. 106, 397 (2002), hep-lat/0110087

View on Pith Pith review arXiv 2002

[114] [114]

S. Kronfeld and S.M. Ryan, Phys. Lett. B543, 59 (2002)

View on Pith 2002

[115] [115]

D. Becirevic et al. , Phys. Lett. B563, 150 (2003)

View on Pith 2003

[116] [116]

C. Davies, Talk given at Flavor Physics and CP Violation (FPCP 2003), Paris, France, 3-6 Jun 2003, hep-ph/0311040

View on Pith Pith review arXiv 2003

[117] [117]

J.L. Rosner, Nucl. Instrum. Meth. A462, 304 (2001)

View on Pith 2001

[118] [118]

ALEPH Collaboration (A. Heister et al. ), Eur. Phys. J. C29, 143 (2003) References 171

View on Pith 2003

[119] [119]

DELPHI Collaboration (P. Abreu et al. ), Eur. Phys. J. C16, 555 (2000); DELPHI Collab- oration (P. Abreu et al. ), Eur. Phys. J. C18, 229 (2000); DELPHI Collaboration (J. Ad- ballah et al. ), Eur. Phys. J. C28, 155 (2003); DELPHI Collaboration (J. Adballah et al. ), Contribution 607 to 30th International Conference on High- Energy Physics (ICHEP 2002), Am...

View on Pith 2000

[120] [120]

OPAL Collaboration (G. Abbiendi et al. ), Eur. Phys. J. C11 587, (1999); OPAL Collab- oration (G. Abbiendi et al. ), Eur. Phys. J. C19, 241 (2001)

View on Pith 1999

[121] [121]

SLD Collaboration (K. Abe et al. ), Phys. Rev. D66, 032009 (2002); SLD Collaboration (K. Abe et al. ), Phys. Rev. D67, 012006 (2003); SLD Collaboration (K. Abe et al. ), SLAC-PUB-8568, Contributed to 30th International Confere nce on High-Energy Physics (ICHEP 2000), Osaka, Japan, 27 Jul - 2 Aug 2000, hep-ex/00120 43

View on Pith 2002

[122] [122]

CDF Collaboration (F. Abe et al. ), Phys. Rev. Lett. 82, 3576 (1999)

View on Pith 1999

[123] [123]

H.G. Moser and A. Roussarie, Nucl. Inst. Meth. A384, 491 (1997)

View on Pith 1997

[124] [124]

D. Abbaneo and G. Boix, J. High Energy Phys. 08, 4 (1999)

View on Pith 1999

[125] [125]

P. Checchia, E. Piotto and F. Simonetto, Contributed t o International Europhysics Con- ference on High-Energy Physics (EPS-HEP 99), Tampere, Finl and, 15-21 Jul 1999, hep- ph/9907300

View on Pith 1999

[126] [126]

A. Ali and M. Misiak, Chapter 6.2 in Ref. [ 9]

View on Pith

[127] [127]

M. Iwasaki (for the Belle Collaboration), Talk given a t 39th Rencontres de Moriond: Electroweak Interactions and Uniﬁed Theories La Thuile, Va l d’Aoste, Italy, 21-28 Mar 2004

View on Pith 2004

[128] [128]

A. Ali, E. Lunghi and A.Y. Parkhomenko, DESY-04-065, h ep-ph/0405075 (2004)

View on Pith 2004

[129] [129]

BABA RCollaboration (B. Aubert et al. ), Phys. Rev. Lett. 89, 201802 (2002)

View on Pith 2002

[130] [130]

Belle Collaboration (K. Abe et al.), BELLE-CONF-0344, Contributed to 21st International Symposium on Lepton and Photon Interactions at High Energie s (LP 03), Batavia, Illinois, 11-16 Aug 2003, hep-ex/0308036

View on Pith Pith review arXiv 2003

[131] [131]

R. Fleischer, Phys. Lett. B365, 399 (1996)

View on Pith 1996

[132] [132]

D. London and A. Soni, Phys. Lett. B407, 61(1997); see also Ref. [ 201]

View on Pith 1997

[133] [133]

Y. Grossman, Z. Ligeti, Y. Nir and H. Quinn Phys. Rev. D68, 015004 (2003)

View on Pith 2003

[134] [134]

M. Gronau, Y. Grossman and J.L. Rosner, Phys. Lett. B579, 331 (2004)

View on Pith 2004

[135] [135]

M. Beneke and M. Neubert, Nucl. Phys. B675 333 (2003)

View on Pith 2003

[136] [136]

BABA RCollaboration (B. Aubert et al. ), BABA R-PUB-04/004, hep-ex/0403026 (2004)

View on Pith Pith review arXiv 2004

[137] [137]

Belle Collaboration (K. Abe et al. ), Phys. Rev. Lett. 91, 261602 (2003)

View on Pith 2003

[138] [138]

M. Verderi (for the BABA RCollaboration), Talk given at 39th Rencontres de Moriond: Electroweak Interactions and Uniﬁed Theories La Thuile, Va l d’Aoste, Italy, 21-28 Mar 2004 172 References

View on Pith 2004

[139] [139]

BABA RCollaboration (B. Aubert et al. ), BABA R-PUB-04-017, hep-ex/0406040 (2004)

View on Pith Pith review arXiv 2004

[140] [140]

BABA RCollaboration (B. Aubert et al. ), Phys. Rev. Lett. 91, 161801 (2003)

View on Pith 2003

[141] [141]

M. Gronau and D. London, Phys. Rev. Lett. 65, 3381 (1990)

View on Pith 1990

[142] [142]

Y. Grossman and H.R. Quinn, Phys. Rev. D58, 017504 (1998)

View on Pith 1998

[143] [143]

J. Charles, Th` ese de l’Universit´ e Paris-Sud, April1999, LPT-Orsay 99-31; available (in French) at http://www.tel.ccsd.cnrs.fr (ID 00002502)

View on Pith

[144] [144]

M. Gronau, D. London, N. Sinha and R. Sinha, Phys. Lett. B514, 315 (2001)

View on Pith 2001

[145] [145]

BABA RCollaboration (B. Aubert et al. ), BABA R-PUB-04-09, hep-ex/0404029 (2004)

View on Pith Pith review arXiv 2004

[146] [146]

BABA RCollaboration (B. Aubert et al. ), Phys. Rev. D69, 031102 (2004)

View on Pith 2004

[147] [147]

BABA RCollaboration (B. Aubert et al. ), Phys. Rev. Lett. 91, 171802 (2003)

View on Pith 2003

[148] [148]

Belle Collaboration (J. Zhang et al. ), Phys. Rev. Lett. 91, 221801 (2003)

View on Pith 2003

[149] [149]

L. Roos (for the BABA RCollaboration), Talk given at 39th Rencontres de Moriond: E lec- troweak Interactions and Uniﬁed Theories La Thuile, Val d’A oste, Italy, 21-28 Mar 2004

View on Pith 2004

[150] [150]

CMD-2 Collaboration (R. Akhmetshin et al. ) Phys. Lett. B578, 285 (2004)

View on Pith 2004

[151] [151]

ALEPH Collaboration (R. Barate et al. ), Z. Phys. C76, 15 (1997)

View on Pith 1997

[152] [152]

A. Falk, Z. Ligeti, Y. Nir and H. R. Quinn, Phys. Rev. D69, 011502 (2004)

View on Pith 2004

[153] [153]

BABA RCollaboration (B. Aubert et al. ), BABA R-CONF-03-004, Contributed to 38th Ren- contres de Moriond on Electroweak Interactions and Uniﬁed T heories, Les Arcs, France, 15-22 Mar 2003, hep-ex/0304030

View on Pith Pith review arXiv 2003

[154] [154]

Belle Collaboration, (K. Abe et al. ), BELLE-CONF-0247, Contributed to 31st Interna- tional Conference on High Energy Physics (ICHEP 2002), Amst erdam, The Netherlands, 24-31 Jul 2002

View on Pith 2002

[155] [155]

Y. Nir, Nucl. Phys. Proc. Suppl. 117, 111 (2003), hep-ph/0208080

View on Pith Pith review arXiv 2003

[156] [156]

Y. Grossman and H. R. Quinn, Phys. Rev. D56, 7259 (1997)

View on Pith 1997

[157] [157]

LASS Collaboration (D. Aston et al. ), Nucl. Phys. B296, 493 (1988)

View on Pith 1988

[158] [158]

J. Charles et al. , Phys. Lett. B425, 375 (1998); Erratum-ibid. B433, 441 (1998)

View on Pith 1998

[159] [159]

C.W. Chiang and L. Wolfenstein, Phys. Rev. D61, 074031 (2000)

View on Pith 2000

[160] [160]

A.S. Dighe, I. Dunietz and R. Fleischer, Eur. Phys. J. C6, 647 (1999)

View on Pith 1999

[161] [161]

B. Kayser, in Proceedings of the 32nd Rencontres de Mor iond on Electroweak Interactions and Uniﬁed Theories, Les Arcs, France, edited by J. Trˆ an Tha nh Vˆ an, Ed. Fronti` eres (1997), p.389; Y.I. Azimov, JETP Lett. 50, 447 (1989); Phys. Rev. D42, 3705 (1990)

View on Pith 1997

[162] [162]

H.R. Quinn, T. Schietinger, J.P. Silva and A.E. Snyder , Phys. Rev. Lett. 85, 5284 (2000)

View on Pith 2000

[163] [163]

Y. Grossman and D. Pirjol, J. High Energy Phys. 006, 029 (2000) References 173

View on Pith 2000

[164] [164]

A.J. Buras and M. Jamin, J. High Energy Phys. 0401, 048 (2004)

View on Pith 2004

[165] [165]

A. J. Buras, F. Schwab and S. Uhlig, TUM-HEP-547, MPP-2 004-47, hep-ph/0405132 (2004)

View on Pith Pith review arXiv 2004

[166] [166]

NA31 Collaboration (G.D. Barr et al. ), Phys. Lett. B317, 233 (1993)

View on Pith 1993

[167] [167]

E731 Collaboration (L.K. Gibbons et al. ), Phys. Rev. D55, 6625 (1997)

View on Pith 1997

[168] [168]

NA48 Collaboration (J.R. Batley et al. ), Phys. Lett. B544, 97 (2002)

View on Pith 2002

[169] [169]

KTeV Collaboration (A. Alavi-Harati et al. ), Phys. Rev. D67, 012005 (2003)

View on Pith 2003

[170] [170]

A. Buras, M. Jamin and M.E. Lautenbacher, Nucl. Phys. B408, 209 (1993)

View on Pith 1993

[171] [171]

M. Ciuchini, E. Franco, G. Martinelli and L. Reina, Phy s. Lett. B301, 263 (1993)

View on Pith 1993

[172] [172]

E. Pallante, A. Pich and I. Scimemi, Nucl. Phys. B617, 441 (2001)

View on Pith 2001

[173] [173]

T. Hambye, S. Peris and E. de Rafael, J. High Energy Phys . 0305, 027 (2003)

View on Pith 2003

[174] [174]

J. Bijnens, E. Gamiz and J. Prades, J. High Energy Phys. 0110, 009 (2001)

View on Pith 2001

[175] [175]

D. Becirevic (for the SPQCDR Collaboration), Nucl. Ph ys. Proc. Suppl. 119, 359 (2003), hep-lat/0209136

View on Pith Pith review arXiv 2003

[176] [176]

CP-PACS Collaboration (S. Aoki et al. ), Nucl. Phys. Proc. Suppl. 106, 332 (2002)

View on Pith 2002

[177] [177]

RBC Collaboration (T. Blum et al. ), Phys. Rev. D68, 114506 (2003)

View on Pith 2003

[178] [178]

M. Golterman and S. Peris, Phys. Rev. D68, 094506 (2003)

View on Pith 2003

[179] [179]

E. Gamiz, J. Prades and I. Scimemi, J. High Energy Phys. 0310, 042 (2003)

View on Pith 2003

[180] [180]

G. Buchalla and A. Buras, Nucl. Phys. B548, 309 (1999)

View on Pith 1999

[181] [181]

W.J. Marciano and Z. Parsa, Phys. Rev. D53, 1 (1996)

View on Pith 1996

[182] [182]

The CKM Collaboration, Proposal to the FNAL PAC, http://www.fnal.gov/projects/ckm/documentation/public/proposal/proposal.html

View on Pith

[183] [183]

T. Inagaki (for the E391 Collaboration), KEK-PREPRIN T-96-181, Talk given at 3rd International Workshop on Particle Physics Phenomenology , Taipei, Taiwan, 14-17 Nov 1996

View on Pith 1996

[184] [184]

The KOPIO Collaboration, RSVP MRE Proposal, http://pubweb.bnl.gov/people/rsvp/proposal.ps

View on Pith

[185] [185]

BABA RCollaboration (B. Aubert et al. ), BABA R-PUB-03-031, hep-ex/0309017 (2003)

View on Pith Pith review arXiv 2003

[186] [186]

Belle Collaboration (P. Krokovny et al. ), Phys. Rev. Lett. 89, 231804 (2002); BABA R Collaboration (B. Aubert et al.), BABAR-CONF-02-034 Contributed to 31st International Conference on High Energy Physics (ICHEP 2002), Amsterdam, The Netherlands, 24-31 Jul 2002, hep-ex/0207053

View on Pith Pith review arXiv 2002

[187] [187]

BABA RCollaboration (B. Aubert et al. ), BABA R-PUB-03-033, hep-ex/0310037 (2003) 174 References

View on Pith Pith review arXiv 2003

[188] [188]

Belle Collaboration (K. Abe et al.), BELLE-CONF-0341, Contributed to 21st International Symposium on Lepton and Photon Interactions at High Energie s (LP 03), Batavia, Illinois, 11-16 Aug 2003, hep-ex/0308048

View on Pith Pith review arXiv 2003

[189] [189]

M. Gronau and D. London, Phys. Lett. B253, 483 (1991)

View on Pith 1991

[190] [190]

M. Gronau and D. Wyler, Phys. Lett. B265, 172 (1991)

View on Pith 1991

[191] [191]

I. Dunietz, Phys. Lett. B270, 75 (1991)

View on Pith 1991

[192] [192]

I. Dunietz, Z. Phys. C56, 129 (1992)

View on Pith 1992

[193] [193]

D. Atwood, I. Dunietz and A. Soni, Phys. Rev. Lett. 78, 3257 (1997); Phys. Rev. D63, 036005 (2001)

View on Pith 1997

[194] [194]

BABA RCollaboration (B. Aubert et al. ), BABA R-PUB-04-002, hep-ex/0402024 (2004)

View on Pith Pith review arXiv 2004

[195] [195]

A. Giri, Y. Grossman, A. Soﬀer and J. Zupan, Phys. Rev. D68, 054018 (2003)

View on Pith 2003

[196] [196]

Belle Collaboration (K. Abe et al.), BELLE-CONF-0343, hep-ex/0308043 (2003); updated analysis presented by A. Poluektof (for the Belle Collabora tion) at 39th Rencontres de Moriond: Electroweak Interactions and Uniﬁed Theories La T huile, Val d’Aoste, Italy, Mar 21-28, 2004

View on Pith Pith review arXiv 2003

[197] [197]

Belle Collaboration (K. Abe et al. ), BELLE-CONF-0343, hep-ex/0406067 (2004)

View on Pith Pith review arXiv 2004

[198] [198]

CLEO Collaboration (H. Muramatsu et al.), Phys. Rev. Lett. 89, 251802 (2002); Erratum- ibid. 90, 059901 (2003); CLEO Collaboration (S. Kopp et al. ), Phys. Rev. D63, 092001 (2001)

View on Pith 2002

[199] [199]

J. Ha ¨ ıssinski, 21st Ecole de Gif (1989), in English, a nd references therein

View on Pith 1989

[200] [200]

M. Pivk, Th` ese de l’Universit´ e Paris VII, May 2003, BABA R-THESIS-03/012, available (in French) at http://tel.ccsd.cnrs.fr (ID 0000 2991)

View on Pith 2003

[201] [201]

BABA R Collaboration (P.F Harrison and H. Quinn eds.), “The BABA R Physics Book: Physics at an Asymmetric B Factory”, SLAC-R-0504 (1998)

View on Pith 1998

[202] [202]

J. Charles, Phys. Rev. D59 054007, (1999)

View on Pith 1999

[203] [203]

S. Gardner, Phys. Rev. D59, 077502 (1999)

View on Pith 1999

[204] [204]

A. H¨ ocker, H. Lacker, M. Pivk and L. Roos, LAL 02-103 (2 002), LPNHE 2002-15; writeup available at http://www.slac.stanford.edu/xorg/ckmﬁtter/ckm talks.html

View on Pith 2002

[205] [205]

M. Gronau and J.L. Rosner, Phys. Rev. D65, 013004 (2002); Erratum-ibid. D65, 079901 (2002)

View on Pith 2002

[206] [206]

R. Fleischer and T. Mannel, Phys. Lett. B397, 269 (1997)

View on Pith 1997

[207] [207]

M. Beneke, G. Buchalla, M. Neubert and C.T. Sachrajda, Phys. Rev. Lett. 83, 1914 (1999)

View on Pith 1999

[208] [208]

M. Beneke, G. Buchalla, M. Neubert and C.T. Sachrajda, Nucl. Phys. B606, 245 (2001)

View on Pith 2001

[209] [209]

M. Pivk and F.R. Le Diberder, LAL 04-10, hep-ph/040626 3, Eur. Phys. J. C39, 397 (2005) References 175

View on Pith 2005

[210] [210]

A.J. Buras and R. Fleischer, Eur. Phys. J. C11, 93 (1999)

View on Pith 1999

[211] [211]

M. Neubert and J.L. Rosner, Phys. Lett. B441, 403 (1998); Phys. Rev. Lett. 81, 5076 (1998)

View on Pith 1998

[212] [212]

J.P. Silva and L. Wolfenstein, Phys. Rev. D49, 1151 (1994)

View on Pith 1994

[213] [213]

R. Fleischer, Phys. Lett. B459, 306 (1999)

View on Pith 1999

[214] [214]

J.D. Bjorken in “New Developments in High Energy Physics” , eds. E.G Floratos and A. Verganelakis, Nucl. Phys. B11 (Proc. Suppl.), 325 (1989)

View on Pith 1989

[215] [215]

M. Neubert and B. Stech, Adv. Ser. Direct. High Energy P hys. 15 294 (1998)

View on Pith 1998

[216] [216]

Y.Y. Keum, H. Li, A.I. Sanda Phys. Lett. B504, 6 (2001)

View on Pith 2001

[217] [217]

M. Ciuchini et al. , Phys. Lett. B515, 33 (2001)

View on Pith 2001

[218] [218]

C.W. Bauer, D. Pirjol, I.Z. Rothstein and I.W. Stewart , MIT-CTP-3469, hep-ph/0401188 (2004)

View on Pith Pith review arXiv 2004

[219] [219]

H. Jawahery, Talk given at 21st International Symposi um on Lepton and Photon Interac- tions at High Energies (LP 03), Batavia, Illinois, 11-16 Aug 2003

View on Pith 2003

[220] [220]

Belle Collaboration (K. Abe et al. ), BELLE-PREPRINT-2004-1, hep-ex/0401029 (2004)

View on Pith Pith review arXiv 2004

[221] [221]

T. Browder, Talk given at 21st International Symposiu m on Lepton and Photon Interac- tions at High Energies (LP 03), Batavia, Illinois, 11-16 Aug 2003

View on Pith 2003

[222] [222]

BABA RCollaboration (B. Aubert et al. ), Phys. Rev. Lett. 91, 021801 (2003)

View on Pith 2003

[223] [223]

T. Tomura (for the Belle Collaboration), Proceedings of 38th Rencontres de Moriond on Electroweak Interactions and Uniﬁed Theories, Les Arcs, Fr ance, 15-22 Mar 2003, hep- ex/0305036

View on Pith 2003

[224] [224]

J. Fry, Talk given at 21st International Symposium on L epton and Photon Interactions at High Energies (LP 03), Batavia, Illinois, 11-16 Aug 2003

View on Pith 2003

[225] [225]

CLEO Collaboration (S. Chen et al. ), Phys. Rev. Lett.85, 525 (2000)

View on Pith 2000

[226] [226]

M. Bona (for the BABA RCollaboration), Talk given at Flavor Physics and CP Violation (FPCP 2003), Paris, France, 3-6 Jun 2003

View on Pith 2003

[227] [227]

BABA RCollaboration (B. Aubert et al. ), Phys. Rev. Lett. 89, 281802 (2001)

View on Pith 2001

[228] [228]

Belle Collaboration (Y. Chao et al.), BELLE-PREPRINT-2003-26, hep-ex/0311061 (2003)

View on Pith Pith review arXiv 2003

[229] [229]

CLEO Collaboration (A. Bornheim et al. ), Phys. Rev. D68, 052002 (2003)

View on Pith 2003

[230] [230]

BABA RCollaboration (B. Aubert et al. ), Phys. Rev. Lett. 91, 241801 (2003)

View on Pith 2003

[231] [231]

CDF Collaboration (C. Paus et al. ), Results prepared for Summer conferences (2003), http://www-cdf.fnal.gov/physics/new/bottom/030529.blessed-bhh/

View on Pith 2003

[232] [232]

A.J. Buras, R. Fleischer, S. Recksiegel and F. Schwab, Phys. Rev. Lett. 92, 101804 (2004); A.J. Buras, R. Fleischer, S. Recksiegel and F. Schwab, CERN- PH-TH-2004-020, hep- ph/0402112 (2004) 176 References

View on Pith 2004

[233] [233]

S. Barshay, L.M. Sehgal and J. van Leusen, Phys. Lett. B591, 97 (2004); A. Ali, E. Lunghi and A.Ya. Parkhomenko, DESY-04-036, hep-ph/0403275 (2004 ); M. Gronau and J.L. Ros- ner, TECHNION-PH-2004-21, hep-ph/0405173 (2004); G. Buch alla and A. Salim Saﬁr, LMU-24-03, hep-ph/0406016 (2004)

View on Pith Pith review arXiv 2004

[234] [234]

L. Roos, Talk given at 2nd Workshop on the CKM Unitarity Triangle, Durham, England, 5-9 Apr 2003, eConf C0304052, WG418

View on Pith 2003

[235] [235]

C.-W. Chiang, M. Gronau, J.L. Rosner and D.A. Suprun, M ADPH-04-1372, hep- ph/0404073 (2004)

View on Pith 2004

[236] [236]

D. Pirjol, Phys. Rev. D60, 054020 (1999)

View on Pith 1999

[237] [237]

M. Gronau and J.L. Rosner, Phys. Rev. D59, 113002 (1999); H.J. Lipkin, Phys. Lett. B445, 403 (1999); J. Matias, Phys. Lett. B520, 131 (2001)

View on Pith 1999

[238] [238]

M. Gronau and J.L. Rosner, Phys. Lett. B572, 43 (2003)

View on Pith 2003

[239] [239]

A.J. Buras, R. Fleischer, S. Recksiegel and F. Schwab, Eur. Phys. J. C32, 45 (2003)

View on Pith 2003

[240] [240]

V. Barger, C.-W. Chiang, P. Langacker, H.S. Lee, MADPH -04-1381, hep-ph/0406126 (2004)

View on Pith Pith review arXiv 2004

[241] [241]

Y. Nir and H.R. Quinn, Phys. Rev. Lett. 67, 541 (1991)

View on Pith 1991

[242] [242]

L. Lavoura, Mod. Phys. Lett. A7, 1553 (1992)

View on Pith 1992

[243] [243]

M. Imbeault, A. St-Laurent Lemerle, V. Page and D. Lond on, Phys. Rev. Lett. 92, 081801 (2004)

View on Pith 2004

[244] [244]

M. Gronau, O.F. Hernandez, D. London and J.L. Rosner, P hys. Rev. D52, 6374 (1995)

View on Pith 1995

[245] [245]

M. Gronau and J.L. Rosner, CLNS 03/1852, TECHNION-PH- 2003-41, To appear in the proceedings of Workshop on the Discovery Potential of an Asy mmetricB Factory at 10 36 Luminosity, Menlo Park, California, 8-10 May 2003, hep-ph/ 0311280 (2003)

View on Pith 2003

[246] [246]

M. Gronau, D. Pirjol and T.M. Yan, Phys. Rev. D60, 034021 (1999); Erratum-ibid. D69, 119901 (2004)

View on Pith 1999

[247] [247]

BABA RCollaboration (B. Aubert et al. ), Phys. Rev. Lett. 91, 201802 (2003); updated results BABA R-PLOT-0055 (2003)

View on Pith 2003

[248] [248]

D. Du, J. Sun, G. Zhu and D. Du, Phys. Rev. D68, 054003 (2003) D. Du, J. Sun, D. Yang and G. Zhu, Phys. Rev. D67, 014023 (2003); D. Du, H. Gong, J. Sun, D. Yang and G. Zhu Phys. Rev. D65, 094025 (2002); Erratum-ibid. D66, 079904 (2002)

View on Pith 2003

[249] [249]

R. Aleksan, P.-F. Giraud, V. Mor´ enas, O. P` ene and A. S . Saﬁr, Phys. Rev. D67, 094019 (2003)

View on Pith 2003

[250] [250]

N. de Groot, W.N. Cottingham and I.B. Whittingham, Con tributed to 38th Rencontres de Moriond on QCD and Hadronic Interactions, Les Arcs, Franc e, 22-29 Mar 2003, hep- ph/0305263 eConf C0304052, WG405

View on Pith 2003

[251] [251]

C.-W. Chiang, M. Gronau, Z. Luo, J.L. Rosner and D.A. Su prun, Phys. Rev. D69, 034001 (2004) References 177

View on Pith 2004

[252] [252]

A. H¨ ocker, M. Laget, S. Laplace and J. von Wimmersperg -Toeller, LAL 03-17 (2003), writeup available at http://www.slac.stanford.edu/xorg /ckmﬁtter/ckm talks.html

View on Pith 2003

[253] [253]

H.R. Quinn and A.E. Snyder, Phys. Rev. D48, 2139 (1993)

View on Pith 1993

[254] [254]

S. Versill´ e, Th` ese de l’Universit´ e Paris-Sud, April 1999; available (in French) at http://www-lpnhep.in2p3.fr/bab ar/public/versille/Thesis/

View on Pith 1999

[255] [255]

Belle Collaboration, (K. Abe et al. ), BELLE-CONF-0318, Contributed to International Europhysics Conference on High-Energy Physics (HEP 2001), Budapest, Hungary, 12-18 Jul 2001

View on Pith 2001

[256] [256]

CLEO Collaboration (C.P. Jessop et al. ), Phys. Rev. Lett. 85, 2881 (2000)

View on Pith 2000

[257] [257]

BABA RCollaboration, (B. Aubert et al. ), BABA R-PUB-03-037, hep-ex/0311049 (2003)

View on Pith Pith review arXiv 2003

[258] [258]

BABA RCollaboration, (B. Aubert et al. ), BABA R-CONF-03-14, Contributed to Interna- tional Europhysics Conference on High-Energy Physics (HEP 2003), Aachen, Germany, 17-23 Jul 2003, hep-ex/0307087

View on Pith Pith review arXiv 2003

[259] [259]

Belle Collaboration (J. Zhang et al. ), Belle-PREPRINT-2004-15, hep-ex/0406006 (2004)

View on Pith Pith review arXiv 2004

[260] [260]

Belle Collaboration (J. Dragic et al. ), BELLE-PREPRINT-2004-14, hep-ex/0405068 (2004)

View on Pith Pith review arXiv 2004

[261] [261]

Belle Collaboration (K. Abe et al. ), BELLE-CONF-0317, Contributed to International Europhysics Conference on High-Energy Physics (HEP 2003), Aachen, Germany, 17-23 Jul 2003

View on Pith 2003

[262] [262]

CLEO Collaboration (E. Eckhart et al. ), Phys. Rev. Lett. 89, 251801 (2002)

View on Pith 2002

[263] [263]

CLEO Collaboration (D.M. Asner et al. ), Phys. Rev. D53, 1039 (1996)

View on Pith 1996

[264] [264]

BABA RCollaboration (B. Aubert et al. ), BABA R-PUB-03-027, hep-ex/0308065 (2003)

View on Pith Pith review arXiv 2003

[265] [265]

Belle Collaboration (K. Abe et al.), BELLE-CONF-0338, Contributed to 21st International Symposium on Lepton and Photon Interactions at High Energie s (LP 03), Batavia, Illinois, 11-16 Aug 2003

View on Pith 2003

[266] [266]

R. Aleksan, F. Buccella, A. Le Yaouanc, L. Oliver, O. P` ene and J.-C. Raynal Phys. Lett. B356, 96 (1995)

View on Pith 1995

[267] [267]

H.J. Lipkin, Y. Nir, H.R. Quinn and A. Snyder, Phys. Rev . D44, 1454 (1991)

View on Pith 1991

[268] [268]

H.R. Quinn and J. Silva, Phys. Rev. D62, 054002 (2000)

View on Pith 2000

[269] [269]

I. Dunietz, H.R. Quinn, A. Snyder, W. Toki and H.J. Lipk in, Phys. Rev. D43, 2193 (1991); A.S. Dighe, I. Dunietz, HJ. Lipkin and J.L. Rosner, Phys. Let t. B369, 144 (1996)

View on Pith 1991

[270] [270]

A.L. Kagan, UCTP-102-04, hep-ph/0405134 (2004)

View on Pith Pith review arXiv 2004

[271] [271]

J. Charles, A. Le Yaouanc, L. Oliver, O. P` ene and J.C. R aynal, Phys. Rev. D60, 014001 (1999)

View on Pith 1999

[272] [272]

M. Zito, Phys. Lett. B586, 314 (2004) 178 References

View on Pith 2004

[273] [273]

M. Ciuchini, E. Franco, G. Martinelli and L. Silvestri ni, Nucl. Phys. B501, 271 (1997); M. Ciuchini, R Contino, E. Franco, G. Martinelli and L. Silve strini, Nucl. Phys. B512, 3 (1998); Erratum-ibid. B531, 656 (1998); M. Ciuchini, E. Franco, G. Martinelli, M. Pieri ni and L. Silvestrini, Phys. Lett. B515, 33 (2001); A. Khodjamirian, Th. Mannel and B. Mel...

View on Pith 1997

[274] [274]

J.F. Donoghue, E. Golowich, A.A. Petrov and J.M. Soare s, Phys. Rev. Lett. 77, 2178 (1996)

View on Pith 1996

[275] [275]

See, e.g., Ref. [ 278] and references therein

View on Pith

[276] [276]

R. Fleischer, G. Isidori and J. Matias, J. High Energy P hys. 0305, 053 (2003)

View on Pith 2003

[277] [277]

J.M. Soares and L. Wolfenstein, Phys. Rev. D47, 1021 (1993)

View on Pith 1993

[278] [278]

Y. Grossman, Y. Nir and M.P. Worah, Phys. Lett. B407, 307 (1997)

View on Pith 1997

[279] [279]

A.L. Kagan and M. Neubert, Phys. Lett. B492, 115 (2000)

View on Pith 2000

[280] [280]

R. Fleischer and T. Mannel, Phys. Lett. B506, 311 (2001)

View on Pith 2001

[281] [281]

D. Atwood and G. Hiller, LMU-09-03, hep-ph/0307251 (2 003)

View on Pith Pith review arXiv

[282] [282]

S. Laplace, Z. Ligeti, Y. Nir and G. Perez, Phys. Rev. D65, 094040 (2002)

View on Pith 2002

[283] [283]

A.I. Sanda, and Z-z. Xing, Phys. Rev. D56, 6866 (1997)

View on Pith 1997

[284] [284]

L. Randall and S. Su, Nucl. Phys. B540, 37 (1999)

View on Pith 1999

[285] [285]

R.N. Cahn and M.P. Worah, Phys. Rev. D60, 076006 (1999)

View on Pith 1999

[286] [286]

G. Barenboim, G. Eyal and Y. Nir, Phys. Rev. Lett. 83, 4486 (1999)

View on Pith 1999

[287] [287]

M. Beneke, G. Buchalla, A. Lenz and U. Nierste, Phys. Le tt. B 576 173 (2003)

View on Pith 2003

[288] [288]

M. Ciuchini, E. Franco, V. Lubicz, F. Mescia and C. Tara ntino, JHEP 0308 031 (2003)

View on Pith 2003

[289] [289]

OPAL Collaboration (G. Abbiendi et al. ), Eur. Phys. J. C12, 609 (2000)

View on Pith 2000

[290] [290]

CLEO Collaboration (D.E. Jaﬀe et al. ), Phys. Rev. Lett. 86, 5000 (2001)

View on Pith 2001

[291] [291]

ALEPH Collaboration (R. Barate et al. ), Eur. Phys. J. C20, 431 (2001)

View on Pith 2001

[292] [292]

BABA RCollaboration (B. Aubert et al. ), Phys. Rev. Lett. 88, 231801 (2002)

View on Pith 2002

[293] [293]

BABA RCollaboration (B. Aubert et al. ), Phys. Rev. Lett. 92, 181801 (2004)

View on Pith 2004

[294] [294]

G.C. Branco, F. Cagarrinho, F. Kr¨ uger, Phys. Lett. B459 224, (1999)

View on Pith 1999

[295] [295]

M. Ciuchini, G. Degrassi, P. Gambino and G.F. Giudice, Nucl. Phys. B534, 3 (1998); A. Ali and D. London, Eur. Phys. J. C9, 687 (1999); A. Ali and D. London Phys. Rept. 320, 79 (1999; A.J. Buras, P. Gambino, M. Gorbahn, S. Jager and L. Silvestrini, Phys. Lett. B500, 161 (2001); A. J. Buras, P. Gambino, M. Gorbahn, S. Jager and L. Silvestrini, Nucl. Phys. B...

View on Pith 1998

[296] [296]

For recent references see, e.g., Y. Grossman, Int. J. M od. Phys. A19, 907 (2004); M. Neu- bert, CLNS-04-1878, hep-ph/0405105 (2004)

View on Pith Pith review arXiv 2004

[297] [297]

C.W. Chiang and J. Rosner, Phys. Rev. D68, 014007 (2003)

View on Pith 2003

[298] [298]

Y. Grossman, G. Isidori and M.P. Worah, Phys. Rev. D58, 057504 (1998); R. Fleischer and T. Mannel, Phys. Lett. B511, 240 (2001); M. Ciuchini and L. Silvestrini, Phys. Rev. Lett. 89, 231802 (2002); see also Ref. [ 300]

View on Pith 1998

[299] [299]

Y. Grossman, A.L. Kagan and Z. Ligeti Phys. Lett. B538, 327 (2002)

View on Pith 2002

[300] [300]

G. Hiller, Phys. Rev. D66, 071502 (2002)

View on Pith 2002