Pith. Sign in

REVIEW

Waiting for the Top Quark Mass, K^+ --> \pi^+ \nu \bar\nu, B_s^0-\bar{B}_s^0 Mixing and CP Asymmetries in B-Decays

PaperPDF from arXiv

data files

ReviewThe objections and verdict, as JSON Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
X Bluesky LinkedIn Reddit Hacker News
A.J. Buras, M.E. Lautenbacher, G. Ostermaier

High Energy Physics - Phenomenology · Submitted 29 Mar 1994 · 51 references

Pith's verdict: The durable contribution is the exact-unitarity (rho-bar, eta-bar) formulation and the analytic toolkit; the numerical predictions are conditional and the x_s number is the soft one.

T0 · AI review

How this review was made: An AI referee (selfhosted/deepseek-v4.1-flash) read the paper on November 11, 2026 and answered a fixed list of questions about it. T0 is the starting level every paper gets. The levels describe how deeply Pith has checked the paper, never the authors.

  1. T0 AI review An AI read the paper and answered a fixed list of questions.
  2. T1 Audit Automatic checks that the references and files the paper relies on exist and match.
  3. T2 Compute The paper's code or calculations re-run with the same results.
  4. T3 Formal statement The claims written out in a formal math language a computer can read.
  5. T4 Proof Those claims proved, and the proof checked by computer.

How Pith checks papers →

· 2 major objections · 7 minor · Ask about this paper · The compiled record · Read the full review →
Challenge this review Comment (0) Read on arXiv ↗
Cite ▾
arXiv IDhep-ph/9403384 (version 1)
Pith IDKOYLLGNF, Pith's permanent record of this paper and its review
CitationA.J. Buras, G. Ostermaier, M.E. Lautenbacher. "Waiting for the Top Quark Mass, K^+ --> \pi^+ \nu \bar\nu, B_s^0-\bar{B}_s^0 Mixing and CP Asymmetries in B-Decays." arXiv:hep-ph/9403384 (1994). https://pith.science/paper/KOYLLGNF
Cite this reviewBibTeX for Pith's review of this paper
Claim paper

Why Pith says this

Highlight any text to comment on it.

Referee report

How Pith checks papers → · Full audit of this paper →

The paper

The paper claims

With tighter inputs on the top mass, $|V_{cb}|$, $|V_{ub}/V_{cb}|$ and the hadronic parameters $B_K$ and $F_Bsqrt{B_B}$, the standard-model unitarity triangle becomes predictive for $sin(2beta)$, $|V_{td}|$, $x_s$ and $BR(K^+ to pi^+ nu bar

The reading

The paper asks a forecasting question: if the top quark mass, $|V_{cb}|$, $|V_{ub}/V_{cb}|$, $B_K$ and $F_Bsqrt{B_B}$ are all measured roughly twice as well by the year 2000 as they were in 1994, how sharply can the quark-mixing triangle and the cleanest rare decays be pinned down? The authors answer with numbers: $sin(2beta) = 0.60 pm 0.14$, $|V_{td}| = (9.5 pm 1.4) times 10^{-3}$, $x_s = 13.3 pm 4.3$ and $BR(K^+ to pi^+ nu bar u) = (1.07 pm 0.24) times 10^{-10}$, while $sin(2alpha)$ and $sin(2gamma)$ stay essentially undetermined. The point of caring is that these four quantities are the targets the B-factory and rare-kaon programmes were being built to hit, so the paper is effectively a statement of what those experiments can and cannot settle before the LHC. The authors also argue that the triangle should be drawn in the rescaled coordinates $bar rho = rho(1 - lambda^2/2)$, $bar eta = eta(1 - lambda^2/2)$, which restores exact unitarity and shifts the apex by a few percent relative to the textbook Wolfenstein picture.

What carries the argument

The carrying object is the rescaled unitarity triangle in the $(bar rho, bar eta)$ plane, obtained by dividing the relation $V_{ud}V^{*}_{ub} + V_{cd}V^{*}_{cb} + V_{td}V^{*}_{tb} = 0$ by $V_{cd}V^{*}_{cb} = -A lambda^3$ so that one side has unit length and the apex sits at $(bar rho, bar eta)$ rather than $(rho, eta)$. Three experimental constraints cut this plane: $epsilon_K$ gives a hyperbola, $x_d$ gives a circle of radius $R_t$ fixed by $sqrt{x_d}$ and the (poorly known) $F_B sqrt{B_B}$, and $BR(K^+ to pi^+ nu bar u)$ gives an ellipse centred near $bar rho = 1$ whose axes are set by the next-to-leading QCD calculation of the decay. The ratio $x_d/x_s$ is the cleanest of these because the top mass and most hadronic uncertainties cancel, leaving $R_t$ in terms of $sqrt{x_d/x_s}$ and a small SU(3)-breaking factor $R_{ds}$. Two compact fits, $S(x_t) approx 0.784 x_t^{0.76}$ and $X(x_t) approx 0.65 x_t^{0.575}$, let the authors turn the numerical scan into analytic formulas accurate to a couple of percent.

Extended reading notes

Core claim

The central claim is conditional and quantitative. Using the standard model with the measured indirect CP violation in $K to pi pi$ ($epsilon_K$) and the measured $B^0_d$ mixing ($x_d$), together with the improved parameter ranges they anticipate, the authors find that the apex of the unitarity triangle is confined enough to predict $sin(2beta)$, $|V_{td}|$, the $B^0_s$ mixing parameter $x_s$ and the branching ratio for $K^+ to pi^+ nu bar u$ at the ten-to-twenty percent level, whereas $sin(2alpha)$ and $sin(2gamma)$ remain spread over nearly their full allowed ranges. They then show that adding a direct measurement of $sin(2alpha)$ or $sin(2gamma)$ to a measurement of $sin(2beta)$ collapses the allowed region dramatically, and that the combination of $BR(K^+ to pi^+ nu bar u)$, $sin(2beta)$, $|V_{cb}|$, $m_t$ and $x_d/x_s$ alone would give a respectable determination of $|V_{td}|$ provided each is measured to about ten percent. Along the way they extend the standard leading-order treatment of the triangle to next order in $lambda = |V_{us}|$, derive closed-form expressions for $sin(2phi_i)$ in terms of $(bar rho, bar eta)$, and give analytic bounds: a lower limit on $m_t$ from $epsilon_K$, a matching lower limit on $B_K$, an upper bound $(sin 2beta)_{max} = 2R_b sqrt{1 - R_b^2}$, and the curve $bar eta = (1 - bar rho)sqrt{bar rho/(2 - bar rho)}$ on which the standard model and superweak models would give indistinguishable $B$-decay asymmetries.

Load-bearing premise

The $x_s$ prediction and the extraction of $R_t$ from $x_d/x_s$ set the SU(3)-breaking ratio $R_{ds} = 1$, i.e. assume $F_{B_s}sqrt{B_{B_s}} = F_{B_d}sqrt{B_{B_d}}$ with equal lifetimes and masses; the paper states this explicitly in Section 5.1 and concedes in Section 5.3 that a ten percent $x_s$ determination requires $R_{ds}$ known to ten percent.

Editorial extensions

If this is right

  • A measurement of $BR(K^+ to pi^+ nu bar u)$ at the ten percent level would either confirm the standard-model prediction of about $1.0 times 10^{-10}$ or expose a discrepancy with the triangle fixed by $epsilon_K$ and $x_d$.
  • A measurement of $sin(2beta)$ near $0.6$ with an error of $pm 0.06$ would already be more informative than the $epsilon_K$ plus $x_d$ prediction, and adding $sin(2alpha)$ at $pm 0.10$ would shrink the allowed region for $delta$, $sin(2gamma)$, $|V_{td}|$, $x_s$ and the kaon branching ratio to a few percent.
  • Because $sin(2alpha)$ and $sin(2gamma)$ cannot be predicted from $epsilon_K$, $x_d$, $|V_{cb}|$ and $|V_{ub}/V_{cb}|$ alone, measuring them is the only way to test whether the standard-model picture holds; a measured value outside the predicted band would be a signal of new physics.
  • Comparing the measured $B^0 to psi K_S$ and $B^0 to pi^+ pi^-$ asymmetries against the curve where $sin(2alpha) = -sin(2beta)$ would let experiment rule out superweak models of CP violation.
  • If $x_s$ is measured to about ten percent and the SU(3)-breaking ratio $R_{ds}$ is known to the same accuracy, $R_t$ and hence $|V_{td}|$ follow without any dependence on the top mass or on $|V_{cb}|$.

Reading between the lines

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

  • The forecast is a snapshot of a moving target: several of the central values quoted here (notably $x_s$ near 13 and $BR(K^+ to pi^+ nu bar u)$ near $1.0 times 10^{-10}$) sit in a region that later data moved away from, so the durable content of the paper is less the numbers than the demonstration that a handful of theoretically clean observables over-determine the triangle.
  • The same logic implies a sharp consistency test: any two of $sin(2beta)$, $BR(K^+ to pi^+ nu bar u)$ and $x_d/x_s$ fix the apex, so a third measurement that misses the intersection is a quantitative handle on new physics rather than a failure of the fit.
  • The paper's insistence that $sin(2alpha)$ and $sin(2gamma)$ are the weak links suggests that the value of a future $B$-factory programme lies mostly in those two angles, since $sin(2beta)$ would already be predicted well by then.
  • Treating the quoted $pm$ as scan half-widths rather than statistical errors means the forecasts are best read as honest ranges of ignorance about the inputs, not as confidence intervals; improving the hadronic inputs is therefore worth more than accumulating events.
Original abstract

Anticipating improved determinations of m_t, |V_ub/V_cb|, B_K and F_B \sqrt{B_B} in the next five years we make an excursion in the future in order to find a possible picture of the unitarity triangle, of quark mixing and of CP-violation around the year 2000. We then analyse what impact on this picture will have the measurements of four possibly cleanest quantities: BR(K^+ --> \pi^+ \nu \bar\nu), x_d/x_s, sin(2\alpha) and \sin(2\beta). Our analysis shows very clearly that there is an exciting time ahead of us. In the course of our investigations we extend the analysis of the unitarity triangle beyond the leading order in \lambda and we derive several useful analytic formulae for quantities of interest.

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.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,815 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.16 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.10 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

Anticipating improved determinations of m_t, |V_ub/V_cb|, B_K and F_B \sqrt{B_B} in the next five years we make an excursion in the future in order to find a possible picture of the unitarity triangle, of quark mixing and of CP-violation around the year 2000. We then analyse what impact on this picture will have the measurements of four possibly cleanest quantities: BR(K^+ --> \pi^+ \nu \bar\nu), x_d/x_s, sin(2\alpha) and \sin(2\beta). Our analysis shows very clearly that there is an exciting time ahead of us. In the course of our investigations we extend the analysis of the unitarity triangle beyond the leading order in \lambda and we derive several useful analytic formulae for quantities of interest.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 Anticipating improved determinations of m_t, |V_ub/V_cb|, B_K and F_B \sqrt{B_B} in the next five years we make an excursion in the future in order to find a possible picture of the unitarity triangle, of quark mixing and of CP-violation around the year 2000. contribution 0.51 0.38 0.06 hedged possibility 0.38
s1 We then analyse what impact on this picture will have the measurements of four possibly cleanest quantities: BR(K^+ --> \pi^+ \nu \bar\nu), x_d/x_s, sin(2\alpha) and \sin(2\beta). contribution 0.67 0.55 0.05 asserted 0.46
s2 Our analysis shows very clearly that there is an exciting time ahead of us. interpretation 0.97 0.68 0.50 asserted 0.99
s3 In the course of our investigations we extend the analysis of the unitarity triangle beyond the leading order in \lambda and we derive several useful analytic formulae for quantities of interest. contribution 0.84 0.95 0.06 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.93 · evidence from proof or derivation 0.84.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
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. Unitarity triangle in the complex (¯̺, η¯) plane. sin(2γ) = 2¯̺η¯ ̺¯ 2 + ¯η 2 = 2̺η ̺ 2 + η 2 (2.19) The lengths CA and BA in the rescaled triangle of fig. 1 to be denoted by Rb and Rt , respectively, are given by Rb ≡ | VudV ∗ ub | | VcdV ∗ cb | = q ̺¯ 2 + ¯η 2 = (1 − λ 2 2 ) 1 λ
Figure 2. Lower bound on BK for | Vub/Vcb |= 0.06 (a), | Vub/Vcb |= 0.08 (b), | Vub/Vcb |= 0.10 (c) from εK and mt < 180 GeV . 4.2 Upper Bound on sin(2β) For the present range of Rb the angle β is smaller than 45o . This allows to derive an upper bound on sin(2β), which depends only on Rb. As shown in fig. 3 it is found to be (sin(2β))max = 2Rb q 1 − R2 b (4.4) Rb βmax (0,0) (1,0)
Figure 3. Determination of (sin(2β))max. This implies (sin(2β))max =    0.795 (βmax = 26.3 o ) | Vub/Vcb | = 0.10 0.663 (βmax = 20.8 o ) | Vub/Vcb | = 0.08 0.513 (βmax = 15.4 o ) | Vub/Vcb | = 0.06 (4.5) 11
Figure 4. Lower bound on FBd p BBd for | Vub/Vcb |= 0.06 (a), | Vub/Vcb |= 0.08 (b), | Vub/Vcb |= 0.10 (c) necessary for ̺¯ ≥ 0. 4.4.2 K+ → π +νν¯ An analogous condition can be derived from the decay K+ → π + q νν¯ by requiring ̺0 2 + (Rbσ) 2 ≥ r0 with ̺0 and r0 defined in (3.19) and (3.21), respectively. Neglecting the tiny contribution of the second term in (3.21), using the formula X(xt) = 0.65 · x 0.575 t (4.10) which reproduces the function X(xt) to an accuracy of 0.5% for the range of mt con￾sidered in this paper and introducing the variable [4] z(K+) = mt ·  Vcb 0.0381
Figure 5. Upper bound on BR(K+ → π +νν¯) for | Vub/Vcb |= 0.06 (a), | Vub/Vcb |= 0.08 (b), | Vub/Vcb |= 0.10 (c) necessary for ̺¯ ≥ 0. 5 Phenomenological Analysis 5.1 First Look In order to describe the situation of 1994 after a possible top quark discovery we make first the following choices for the relevant parameters: Range I |Vcb| = 0.038 ± 0.004 | Vub/Vcb | = 0.08 ± 0.02 BK = 0.7 ± 0.2 q BBd FBd = (200 ± 30) MeV xd = 0.72 ± 0.08 mt = (165 ± 15) GeV (5.1) The values of | Vcb | and | Vub/Vcb | given here are consistent with the recent summary in [41]. The values of BK cover comfortabl
Figure 6. Unitarity triangle in the (¯̺, η¯) plane determined by εK, | Vub/Vcb | and xd using ranges (I)–(III) as of eqs. (5.1), (5.4) and (5.5), respectively. xs = ( 13.3 ± 4.3 (range II) 12.9 ± 2.8 (range III) (5.9) BR(K+ → π +νν¯) = ( (1.07 ± 0.24) · 10−10 (range II) (1.03 ± 0.15) · 10−10 (range III) (5.10) This exercise implies that if the accuracy of various parameters given in (5.4) and (5.5) is achieved the determination of | Vtd | and the predictions for sin(2β) and BR(K+ → π +νν¯) are quite accurate. A sizable uncertainty in xs remains however. Another important message from this
Figure 7. Determination of the unitarity triangle in the (¯̺, η¯) plane by measuring sin(2β) and sin(2α) as of eqs. (5.11) and (5.12), respectively. For sin(2α) we always find two solutions in (¯̺, η¯) and for sin(2β) we only use the solution consistent with | Vub/Vcb |≤ 0.1. and give in tab. 5 the predicted ranges for δ, sin(2γ), BR(K+ → π +νν¯), | Vtd | and xs corresponding to the values of sin(2β) and sin(2α) given in (5.14) and | Vcb |, xd and mt of (5.4). We use only the solution of sin(2β) consistent with | Vub/Vcb |≤ 0.1. It should be stressed that this impressive accuracy can only be…
Figure 8. Determination of the unitarity triangle in the (¯̺, η¯) plane by measuring sin(2β) and sin(2γ) as of eqs. (5.11) and (5.13), respectively. For sin(2γ) we always find two solutions in (¯̺, η¯) and for sin(2β) we only use the solution consistent with | Vub/Vcb |≤ 0.1. 5.5 K+ → π +νν¯, sin(2β), | Vcb |, mt and xd/xs We would like to address now our last question posed in the introduction: How well should one measure BR(K+ → π +νν¯), sin(2β), | Vcb |, mt and xd/xs in order to obtain an acceptable determination of the CKM matrix on the basis of these five quantities alone. As we stated at
Figure 9. Allowed ranges in the (¯̺, η¯) plane with constraints from eqs. (5.15) and (5.16) for BR(K+ → π +νν¯) and Rt = 1.0 ± 0.1. with the results of the independent measurements of sin(2β) = 0.60±0.06 and sin(2α) given by (5.12). The latter are represented by dark shaded rectangles. The black rectangles illustrate the accuracy of future LHC measurements (∆ sin(2α) = ±0.04, ∆ sin(2β) = ±0.02) [28]. -1.0 -0.5 0.0 0.5 1.0 sin2α -1.0 -0.5 0.0 0.5 1.0 sin2β -1.0 -0.5 0.0 0.5 1.0 sin2β -1.0 -0.5 0.0 0.5 1.0 sin2α (I) (II) (III) (IV) superweak
Figure 10. sin(2α) versus sin(2β) plot corresponding to the parameter ranges I-IV as of (5.1), (5.4), (5.5) and (5.17) and the dark shaded rectangles given by (5.12) and (5.11) (b). The black rectangles illustrate the accuracy of future LHC measurements. We also show the results of an analysis in which the accuracy of various parameters is as in (5.4) but with the central values modified: 23

Figures reproduced from arXiv:hep-ph/9403384 by the authors.

References
How later papers used it

58 later papers cite it

Evidence: substantial. 51 of the citing papers share no author with it, and 14 of those carry a confident label from Pith's citation classifier.

Pith read 12 of the 72 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

Uses its method or tool 2 of 10 papers with this label

  • Adopted this paper's definition of the Wolfenstein parameters to keep the CKM matrix unitary to all orders of lambda.

    A Revisit to Top Quark Forward-Backward Asymmetry (2011) · 0.92 · paraphrased: the licence does not allow quoting

  • Followed this paper to define its parameters, noting that V_ub is typically taken of order lambda^3 though numerically of order lambda^4.

    How much space is left for a new family? (2009) · 0.89 · paraphrased: the licence does not allow quoting

How the literature uses it

49 arXiv papers cite this in 62 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 · 42 sentences without a confident label

Builds on it 1 paper
  • The value of $sin2β$ from Table [ref] implies $β=(21.5±1.0)^∘$ or [equation] In terms of the improved Wolfenstein parameters $ρ̅$ and $η̅$ [ref] the unitarity triangle is then determined by [equation] [equation] These formulas have been derived in [ref] for $B→π^+π^-$, but they apply to the case of $B→ρ^+_Lρ^-_L$ as well.

    B -> V_L V_L Decays at Next-to-Leading Order in QCD · Determination of $ρ̅$, $η̅$, $γ$ and $α$ · 0.87

Uses its method or tool 8 papers
  • In finding the $$-independent correlations between various observables it is useful to use the so-called improved Wolfenstein parametrization [ref] of the CKM matrix that is much more precise than the original Wolfenstein parametrization [ref] .

    Searching for New Physics in Rare $K$ and $B$ Decays without $|V_{cb}|$ and $|V_{ub}|$ Uncertainties · A Useful Parametrization of the UT · 0.88

  • If we make use of the unitarity of the CKM matrix and apply the Wolfenstein parametrisation [ref] as generalised in Ref. [ref] , we can write ([ref]) as [equation] Here [equation] and [equation] are CP-conserving, “hadronic" parameters, where [equation] with $λ≡|V_us|=0.22521±0.00083$ are CKM parameters.

    Extracting gamma and Penguin Topologies through CP Violation in B_s^0 -> J/psi K_S · The Basic Strategy · 0.80

  • Given that $s_13≪s_23 ≪s_12 ≪1$, a perturbative expansion in powers of the sine of the Cabibbo angle $s_12$ can be performed [ref] , defining [equation] and imposing the unitarity constraint at the desired order [ref] .

    Effective Theories for Quark Flavour Physics · The Cabibbo-Kobayashi-Maskawa mixing matrix · 0.89

Uses its data or values 2 papers
  • Including the dominant corrections [ref] with the Wolfenstein parameters taken from global unitarity fits by CKMFitter [ref] (using values from the January 2022 update) gives [equation] using $=0.97367(32)$ from superallowed $0^+→0^+$ nuclear $β$ decays [ref] and $=0.22330(53)$ from $K_ℓ3$ decays [ref] .

    D-meson semileptonic decays to pseudoscalars from four-flavor lattice QCD · Tests of CKM unitarity · 0.94

  • Since it is better suited for our purpose, we adopt the Wolfenstein-like but exactly unitary parametrization of [ref] , for which we obtain up-to-date values for the parameters $λ=0.22481±0.00059$, $A=0.817±0.018$, $ρ=0.145±0.015$ and $η=0.366±0.012$ by performing our own fit to PDG data [ref] .

    The Basis Invariant Flavor Puzzle · Quark sector flavor invariants · 0.87

Cites it as background 9 papers
  • It was pointed out [ref] that as in any perturbative expansion, high order terms in $λ$ are not unique in the Wolfenstein parametrization, though the nonuniqueness of the high order terms does not change the physics.

    Wolfenstein Parametrization at Higher Order: Seeming Discrepancies and Their Resolution · Introduction · 0.81

  • The dominance of B physics constraints in the past decades has dictated the traditional presentation of consistency between observables, in the complex plane given by [ref] ,

    Natural complex plane for kaon CKM data: framework, status and future · Introduction · 0.81

  • In the Standard Model (SM), the complex phases $ϕ_d$ and $ϕ_s$ associated with the mixing between neutral $B_q^0$ and $B̅_q^0$ mesons, where $q∈{d,s}$, are parametrised as [equation] Their experimental determinations are powerful probes to search for evidence of physics beyond the Standard Model (BSM): The measurement of $ϕ_d$ constrains the angle $β$ of the Unitarity Triangle (UT), and the value of $ϕ_s$ can directly be compared with the SM prediction based on the Wolfenstein parametrisation [ref] of the Cabibbo–Kobayashi–Maskawa (CKM) quark-mixing matrix [ref] .

    Taming Penguins: Towards High Precision Measurements in $\phi_d$ and $\phi_s$ · Introduction · 0.98

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.