Theoretical Uncertainties and Phenomenological Aspects of $B \rightarrow X_s \gamma$ Decay

A. J. Buras; M. Misiak; M. Muenz; S. Pokorski

REVIEW

Theoretical Uncertainties and Phenomenological Aspects of $B \rightarrow X_s \gamma$ Decay

A. J. Buras, M. Misiak, M. Muenz, S. Pokorski

High Energy Physics - Phenomenology · Submitted 23 Nov 1993 · 42 references

Pith's verdict: An honest, influential paper: it correctly identifies the renormalization-scale dependence as the dominant error in leading-order B→X_sγ and correctly weakens the 2HDM bounds, but the ±25% is an estimator rather than a derived bound.

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arXiv IDhep-ph/9311345 (version 2)

Pith IDU66NBAAT, Pith's permanent record of this paper and its review

CitationA. J. Buras, M. Misiak, M. Muenz, S. Pokorski. "Theoretical Uncertainties and Phenomenological Aspects of $B \rightarrow X_s \gamma$ Decay." arXiv:hep-ph/9311345 (1993). https://pith.science/paper/U66NBAAT

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Editor's note

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The thing to know: this is the paper that told the field its B→X_sγ prediction was not as precise as the exclusion plots implied. The leading-log formula itself is assembled from refs. [3]–[9] and the authors say so. What is theirs is the error budget in section 2 — six sources enumerated and sized, with the μ-dependence identified as dominant at roughly ±25% when μ is varied by a factor of two around m_b — and the consequent retreat from the tight 2HDM exclusions of Hewett and of Barger-Berger-Phillips. That retreat is correct and was needed. Section 4 is the other real contribution: a clean statement of what a full next-to-leading calculation requires (two-loop (Q7,Q8) mixing, three-loop mixing between the four-quark and magnetic sectors, O(α_s) matching), plus the scheme-independence argument for C7^eff in eqs. 31–38 and the cancellation structure of eq. 44. That section has been the roadmap for the subsequent decade of calculations, and it holds up on rereading. The appendix is candid about the γ57, γ58, γ68 disagreements in the literature and quantifies their effect at about 1%, which is the right way to handle a disputed input. On the soft spots, the stress-test note is right and the authors already concede the point: the factor-of-two μ variation is an estimator, and the r27 toy scan in section 4 is a one-parameter check of a six-parameter space. A correlated shift across several r_i7 at their O(1) range could move the central value further than the dashed curves suggest. But note the direction — a larger NLL shift widens the error bars and weakens the bounds further, which reinforces rather than undercuts the headline. So this bears on the precise size of the bars in figs. 3–8, not on the conclusion. The ±10% spectator-model error in section 2(i) is likewise hand-set with no derivation, and the 2× error-bar exclusion convention of eq. (14) drives the 'significantly weaker' language; fig. 8 shows the 1× and 0× variants, so it is disclosed. One correction to the record: the classifier reports no stated limitations, which is wrong — section 4 states them explicitly. Who should read it: anyone working on rare B decays or on 2HDM constraints, and anyone who wants a model of how to present a theory-error budget honestly. Yes to referees.

Referee report

Significance

This is a timely and carefully argued paper, and its main qualitative claim — that the scale uncertainty dominates and that the b→sγ bounds on the 2HDM must therefore be relaxed relative to refs. [30,31] — is well supported and was important for the field. The paper's strengths deserve explicit credit: the scheme-independence argument for C_7^eff in eqs. (31)–(38) is clean and non-trivial; the NLL bookkeeping in eqs. (24)–(28) and (44) is explicit enough to be checked; the falsifiable projection that a complete NLL calculation will bring the residual μ-dependence below 5% is a genuine prediction; and fig. 8's three curves (2σ, 1σ, no error) show unusual candour about how the bounds depend on the treatment of errors. The paper is also candid about its own limitations — contrary to the classifier record, which reports none — stating plainly in §4 that 'we still do not know which of the dashed curves in fig. 2 is closest to the true next-to-leading result.' That candour is a mark in the paper's favour.

Major objections (2)

[§5, conclusion (v), with §4 and fig. 2] The concluding statement that 'once a next-to-leading result is found, its μ-dependence should be below 5%, for μ changing from m_b/2 to 2m_b' is stronger than the exercise of §4 supports. That exercise sets Ĵ = 0 and C^(1) = 0 in eqs. (24) and (30), and sets every r_i7 to zero except r_27. The residual μ-dependence after the cancellation in eq. (44) is controlled precisely by the quantities that were set to zero: the two-loop (Q_7,Q_8) anomalous dimensions of item (i), the three-loop mixing of item (ii), and the O(α_s) matching corrections of item (iii). The dashed curves of fig. 2 therefore illustrate the mechanism of cancellation but do not bound the leftover. I would ask the authors to restate conclusion (v) conditionally — for instance, that the residual μ-dependence should fall below 5% provided the omitted NLL constants are of order one and not strongly correlated — rather than as a derived result.
[§2 point (v), §3, eqs. (13)–(14), figs. 4, 7 and 8] The ±25% scale error is the single number that sets every bound quoted in the abstract and drawn in figs. 4, 7 and 8, and the authors themselves describe it as an estimate rather than a derivation. Because the estimator is heuristic, the reader cannot judge how the 2HDM lower bound on M_H± would move if the true NLL shift were, say, ±15% or ±40%. A short table, or one extra pair of curves in figs. 7 and 8, showing the bound for two alternative error sizes would make the abstract's claim that the 2HDM bounds are 'significantly weaker than the ones present in the recent literature' quantitatively checkable. The direction of the concern is favourable to the paper — a larger error weakens the bound further, so the qualitative conclusion is robust — but the quantitative size of the weakening is the paper's headline and should be displayed with its sensitivity.

Minor objections (9)

[§2, eq. (11)] The numerical decomposition of C_7^eff into its three contributions is helpful; consider quoting the same three numbers for m_t = 200 GeV alongside the m_t = 130 GeV case, so that the reader can see how the relative weight of the C_7, C_8 and C_2 terms evolves with the top mass.
[§2, point (ii)] The text first states 'we will use z = 0.316 ± 0.013' and then adds 'even if one assumes that the error due to z is twice larger than 6%'. Please state explicitly which value of the z error actually enters the quadrature sum used for the error bars of fig. 3, since the two sentences leave it ambiguous.
[§3, eq. (17) and the following paragraph] The sentence 'for tanβ = 2 which is large enough to make the terms proportional to 1/tan²β in eq. (17) practically irrelevant' would be more convincing with a number. At tanβ = 2 the coefficient is 1/4, and the bracket multiplying it has the same structure as the Standard Model C_7 up to a factor of 1/3, so the term is a few percent of ΔC_7 rather than negligible; stating its size would let the reader judge whether the tanβ-independence claimed for tanβ > 2 in fig. 7 is adequate.
[Fig. 7] The Z→b b̄ curve is drawn for m_t = 150 GeV only, while the b→sγ curves are shown for three top masses; please label the Z→b b̄ curve with its top mass on the figure itself and note in the caption that the comparison is not at fixed m_t.
[Fig. 2] The three dashed curves are not identified. Please add a legend or a caption note stating which curve corresponds to r_27 = −2, which to 0, and which to +2, so that the reader can connect the figure to the text of §4.
[§4, eq. (44)] The sum over i in the second term is left implicit, and the equation mixes effective coefficients in the first term with ordinary coefficients in the second. Footnote 10 explains the distinction, but writing the sum as an explicit Σ_i and adding a parenthetical reminder in the equation would make eq. (44) self-contained.
[§4, item (iii)] Ref. [37] (Adel and Yao, UM-TH-93-20) is cited as an attempt at the two-loop matching calculation; since it is a preprint, please mark it as such in the reference list so that the status of item (iii) is unambiguous.
[Appendix, eq. (49)] The entries rendered as '41681u − 23281d' and '−44881u + 20081d' should be typeset as explicit fractions (416/81 u − 232/81 d and so on); in the present form they read as products of integers and are easy to misparse.
[§3, eq. (18)] The b→c τ ν̄_τ bound is quoted without stating that it assumes the Model II pattern of charged-Higgs couplings; please add that qualifier so the reader knows the bound does not apply to a general 2HDM.

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The paper

The paper claims

The largest error in the predicted $B$→$X_s$γ rate is the choice of renormalization scale, not new physics.

The reading

This paper asks how much of the theoretical error in the predicted inclusive branching ratio for $B$→$X_s$γ is real physics and how much is an artifact of stopping at leading logarithmic order. Its answer is that the largest single uncertainty is the dependence on the renormalization scale $m_b$, which moves the prediction by roughly $m_b$ when that scale is varied by a factor of two in either direction around $m_b$ — larger than the spectator-model, CKM, phase-space, and strong-coupling errors put together. Because that band is wide, the measured $b$→$s$γ rate cannot yet pin down Standard Model parameters, and the charged-Higgs mass limits quoted by other authors have to be relaxed. The paper then sets out, step by step, what a complete next-to-leading order calculation would require, and shows with a partial exercise that such a calculation should shrink the scale dependence to a few percent. Along the way it maps the region of the charged-Higgs mass versus $m_b$ plane that $b$→$s$γ, $Z$→$b$b̄ and $b$→$c$τν̄τ together still exclude.

What carries the argument

The argument is carried by the effective hamiltonian built from eight operators — four-quark current-current and penguin operators $Q_1$ through $Q_6$, plus the magnetic penguin operators $Q_7$ and $Q_8$ — together with their Wilson coefficients. Two devices do the work. First, the authors define scheme-independent effective coefficients $C_7^{eff}$ and $C_8^{eff}$ that absorb the one-loop matrix elements of the four-quark operators, which in some regularization schemes do not vanish for an on-shell photon; this makes the leading-order result regularization-independent and explains why the QCD mixing between the four-quark and magnetic sectors, normally a higher-order effect, appears already at leading order. Second, they write the renormalization group evolution matrix as a leading-order factor bracketed by next-to-leading corrections summarized in a matrix $m_b$, whose entries are fixed by the two-loop anomalous dimension matrix and the one-loop $\beta$ function. Expanding the evolution of the operator matrix elements around $m_b$ then produces explicitly the $m_b$ terms that cancel the scale dependence of the coefficients, leaving only unknown constants $r_{i7}$ from the two-loop on-shell matrix elements. Setting all $r_{i7}$ to zero except $r_{27}$, which they vary over $-2$, $0$ and $2$, produces the dashed curves of their figure and the estimate that the scale uncertainty falls from about $m_b$ to about $m_b$.

Extended reading notes

Core claim

The central claim is that the leading-order prediction for the inclusive $B$→$X_s$γ branching ratio is dominated by a theoretical systematic — its dependence on the renormalization scale $m_b$ — and that this systematic is large enough to change the phenomenological conclusions drawn from the existing measurement. Concretely, varying $m_b$ by a factor of two around $m_b$ changes the predicted ratio by about $m_b$, so the ratios obtained at $m_b$ and $m_b$ differ by a factor of about 1.6. The authors argue that this is the appropriate way to size the unknown next-to-leading corrections, and they show that once those corrections are included the leading scale dependence cancels against logarithms from the next-to-leading matrix elements, leaving a residual dependence one order higher. The phenomenological consequence they draw is that the current data do not usefully restrict Standard Model parameters beyond other experiments, while the two-Higgs-doublet bounds, though weakened relative to earlier literature, remain strong and, when combined with $Z$→$b$b̄ and $b$→$c$τν̄τ, still give the most restrictive exclusion in the $M_{H^±}$–$m_b$ plane.

Load-bearing premise

The load-bearing premise is that varying the renormalization scale by a factor of two in each direction around $m_b$ correctly estimates the size of the unknown next-to-leading corrections; the authors acknowledge that their partial exercise cannot replace the full calculation and that they do not know which of the resulting curves is closest to the truth, yet every error bar and every weakened bound in the paper inherits that estimate.

Editorial extensions

If this is right

A complete next-to-leading calculation — two-loop mixing in the $(Q_7,Q_8)$ sector, three-loop mixing between the four-quark and magnetic sectors, and the $O(α_s)$ matching corrections to $C_7(M_W)$ and $C_8(M_W)$ — should reduce the scale dependence to below 5% for $m_b$ between $m_b/2$ and $2m_b$, which is the threshold at which the prediction becomes sharp enough to compete with other constrain
If the inclusive rate is eventually measured near the present upper bound of $5.4×10^{-4}$, a lower bound on the top quark mass as a function of $α_s(M_Z)$ becomes meaningful; an upper bound below 200 GeV follows only if the rate comes in below roughly $1.7×10^{-4}$.
For charged Higgs masses above roughly 600 GeV, the two-Higgs-doublet and Standard Model predictions cannot be separated at the present level of theoretical accuracy, independently of how precise the measurement becomes.
In the two-Higgs-doublet model the $b$→$s$γ bound on $M_{H^±}$ becomes essentially independent of $m_b$ once $m_b$ exceeds about 2, so the exclusion can be plotted as a single curve in the $m_t$–$M_{H^±}$ plane.
The three processes $b$→$s$γ, $Z$→$b$b̄ and $b$→$c$τν̄τ are together sufficient to give the most restrictive bounds in the $M_{H^±}$–$m_b$ plane; other flavour-changing neutral current constraints are weaker.

Reading between the lines

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

The paper's own logic implies that any future claim of a two-Higgs-doublet or supersymmetric signal in $b$→$s$γ must quote the scale band alongside the central value; otherwise the purported signal lies inside the theory error and is not a signal at all.
Replacing the factor-of-two heuristic with a genuine error bar requires the constants $r_{i7}$ from the two-loop on-shell matrix elements, so that single calculation is the pivot on which this channel's competitiveness with $Z$→$b$b̄ turns.
Because the toy exercise varied only $r_{27}$ and set the remaining $r_{i7}$ to zero, the residual few-percent spread it finds is plausibly an underestimate; the true next-to-leading spread should not be trusted until the $(Q_7,Q_8)$ two-loop mixing and the other constants are known.
The same scale-setting bookkeeping applies directly to the Minimal Supersymmetric Standard Model, since the paper notes that the leading-order formulae are unchanged there and only the matching coefficients differ; the $m_b$ band quoted here therefore transfers to supersymmetric parameter scans without recomputation.

Original abstract

We analyze uncertainties in the theoretical prediction for the inclusive branching ratio $BR[B \rightarrow X_s \gamma]$. We find that the dominant uncertainty in the leading order expression comes from its $\mu$-dependence. We discuss a next-to-leading order calculation of $B \rightarrow X_s \gamma$ in general terms and check to what extent the $\mu$-dependence can be reduced in such a calculation. We present constraints on the Standard and Two-Higgs-Doublet Model parameters coming from the measurement of $b \rightarrow s \gamma$ decay. The current theoretical uncertainties do not allow one to definitively restrict the Standard Model parameters much beyond the limits coming from other experiments. The bounds on the Two-Higgs-Doublet Model remain very strong, though significantly weaker than the ones present in the recent literature. In the Two-Higgs-Doublet Model case, the $b \rightarrow s \gamma$, $Z \rightarrow b \bar{b}$ and $b \rightarrow c \tau \bar{\nu}_{\tau}$ processes are enough to give the most restrictive bounds in the $M_{H^{\pm}}-tan \beta$ plane.

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, 5,688 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.02 · states limitation 0.92 · human participants 0.01 · controlled comparison 0.05 · randomized assignment 0.01 · states quantitative result 0.16 · compares with prior results 0.90 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

We analyze uncertainties in the theoretical prediction for the inclusive branching ratio $BR[B \rightarrow X_s \gamma]$. We find that the dominant uncertainty in the leading order expression comes from its $\mu$-dependence. We discuss a next-to-leading order calculation of $B \rightarrow X_s \gamma$ in general terms and check to what extent the $\mu$-dependence can be reduced in such a calculation. We present constraints on the Standard and Two-Higgs-Doublet Model parameters coming from the measurement of $b \rightarrow s \gamma$ decay. The current theoretical uncertainties do not allow one to definitively restrict the Standard Model parameters much beyond the limits coming from other experiments. The bounds on the Two-Higgs-Doublet Model remain very strong, though significantly weaker than the ones present in the recent literature. In the Two-Higgs-Doublet Model case, the $b \rightarrow s \gamma$, $Z \rightarrow b \bar{b}$ and $b \rightarrow c \tau \bar{\nu}_{\tau}$ processes are enough to give the most restrictive bounds in the $M_{H^{\pm}}-tan \beta$ plane.

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 analyze uncertainties in the theoretical prediction for the inclusive branching ratio $BR[B \rightarrow X_s \gamma]$.	contribution 1.00	0.92	0.05	asserted 0.83
s1	We find that the dominant uncertainty in the leading order expression comes from its $\mu$-dependence.	result 1.00	0.94	0.18	asserted 1.00
s2	We discuss a next-to-leading order calculation of $B \rightarrow X_s \gamma$ in general terms and check to what extent the $\mu$-dependence can be reduced in such a calculation.	contribution 0.70	0.85	0.07	asserted 0.50
s3	We present constraints on the Standard and Two-Higgs-Doublet Model parameters coming from the measurement of $b \rightarrow s \gamma$ decay.	contribution 0.69	0.86	0.14	asserted 1.00
s4	The current theoretical uncertainties do not allow one to definitively restrict the Standard Model parameters much beyond the limits coming from other experiments.	interpretation 0.48	0.51	0.33	asserted 0.97
s5	The bounds on the Two-Higgs-Doublet Model remain very strong, though significantly weaker than the ones present in the recent literature.	result 0.91	0.76	0.18	asserted 1.00
s6	In the Two-Higgs-Doublet Model case, the $b \rightarrow s \gamma$, $Z \rightarrow b \bar{b}$ and $b \rightarrow c \tau \bar{\nu}_{\tau}$ processes are enough to give the most restrictive bounds in the $M_{H^{\pm}}-tan \beta$ plane.	result 0.94	0.74	0.15	asserted 0.99

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from proof or derivation 0.54.

What was examined, and what was not

sources read

arXiv listing abstract v2

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.** Leading order one loop diagrams generating the

**Figure 2.** µ-dependence of the theoretical prediction for the ratio R, for mt=150 GeV and αs(MZ) = 0.12. The solid line corresponds to the leading order prediction. The dashed lines describe possible next-to-leading results (see section 4). One can see that when µ is varied by a factor of 2 in both directions around mb ≃ 5 GeV , the ratio (4) changes by around ±25%, i.e. the ratios R obtained for µ = 2.5 GeV and µ = 10 GeV differ by a factor of 1.6. This is in a rough agreement with what has been found in ref. [11]. In section 4 we will argue why varying µ by a factor of 2 in both directions…

**Figure 3.** Predictions for B → Xsγ in the SM, as a function of the top quark-mass, with the theoretical uncertainties taken into account (see the text). may tell us something about the SM parameters

**Figure 4.** presents the lower limits on the top-quark mass following from the assumption that the future experimental result will satisfy the inequality BRtheor[B → Xsγ] + 2 ×

**Figure 5.** Charged scalar exchanges contributing to

**Figure 6.** Predictions for B → Xsγ in the 2HDM, as a function of the top-quark mass, with the theoretical uncertainties taken into account (see the text). For most of the top-quark masses, the results for MH± = 100GeV in fig. 6 are in contradiction with present measurements, even if the theoretical uncertainties are taken into account. On the other hand, comparing figs. 3 and 6 we can conclude that in the MH± = 600GeV case we are not able to distinguish between the SM and the 2HDM, independently of the accuracy of future measurements (but assuming the present accuracy of the theoretical…

**Figure 7.** presents the limits in the tanβ-MH± plane, obtained by assuming that the excluded values of tanβ and MH± are those for which the inequality (14) holds. The presented limits are found with help of the experimental input from eq. (3). The three solid curves represent lower bounds on MH± obtained from b → sγ for three different values of the top quark mass: 120, 150 and 210 GeV. The dashed curves show bounds coming from the Z → b ¯b and b → cτν¯τ decays. The shown Z → b ¯b bound is based on the results of ref. [27] and corresponds to mt = 150 GeV . The b → cτν¯τ bound is given by the…

**Figure 8.** The b → sγ lower limits for the charged Higgs boson mass as functions of mt for tan β = 2. See the text for the description of the curves. The solid line in this figure shows the lower bound for MH± obtained using the requirement described in eq. (14). If we require the theoretical prediction for BR[B → Xsγ ] be only one, not two error bars away from the experimental upper limit, then our lower bound on MH± is described by the dashed curve in fig. 8. The dotted line in this figure corresponds to assuming that the theoretical prediction is given by its central value, with no…

Figures reproduced from arXiv:hep-ph/9311345 by the authors.

References

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View on Pith 1992
[35]

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View on Pith 1981
[36]

M. Misiak and M. M¨ unz, in preparation

View on Pith
[37]

K. Adel and Y.P. Yao, preprint UM-TH-93-20 (hep-ph 9308 349)

View on Pith
[38]

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View on Pith 1972
[39]

M. Misiak, preprint TUM-T31-46/93 (hep-ph 9309236)

View on Pith
[40]

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

View on Pith 1993
[41]

N. Cabibbo and L. Maiani, Phys. Lett B79 (1979) 109; C. S. Kim and A. D. Martin, Phys. Lett. B225 (1989) 186 21

View on Pith 1979
[42]

S. Wolfram, Mathematica, Addison-Wessley Publ. Comp., N.Y. 1988. 22

View on Pith 1988

Forward citations

Cited by 32 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. OpenAlex reports about 382 citations worldwide. Full citation record

The (Q_7,Q_{1,2}) contribution to B -> X_s gamma at O(alpha_s^2)
hep-ph 2015-03 accept novelty 7.0 of 10

The O(alpha_s^2) contribution of Q7-Q1,2 interference to B -> X_s gamma is computed at m_c = 0 and combined with the heavy-charm limit to give B_s gamma = (3.36 +/- 0.23) x 10^-4 in the Standard Model.
Factorization at Subleading Power and Irreducible Uncertainties in $\bar B\to X_s\gamma$ Decay
hep-ph 2010-03 conditional novelty 7.0 of 10

Resolved-photon contributions in B-bar to X_s gamma obey a new factorization formula with extra soft and jet functions, and generate non-local 1/m_b corrections that leave an irreducible about 5 percent theory uncerta...
Electroweak Baryogenesis in Supersymmetric Models
hep-ph 1995-07 conditional novelty 7.0 of 10

Sufficient baryon asymmetry to explain the observed universe can be generated during the electroweak phase transition in supersymmetric models if new CP-violating phases are 10^-2 to 10^-4 and some superpartners are light.
Electric Dipole Moments in the CP-violating Generational Three-Higgs-Doublet Model
hep-ph 2026-09 conditional novelty 6.0 of 10

In the CP-violating G3HDM, EDMs of the b quark, neutron, and mercury are controlled by top-enhanced charged-Higgs loops, while nearly degenerate neutral Higgs pairs enforce pairwise cancellations that suppress the c q...
Precision tests of third-generation four-quark operators: $gg \to h$ and $h \to \gamma \gamma$
hep-ph 2025-07 conditional novelty 6.0 of 10

Two-loop SMEFT corrections from third-generation four-quark operators to gg to h and h to gamma gamma are computed with full mass dependence, including new two-loop anomalous dimensions.

Show 27 more citing papers

Light Scalars in the Extended Georgi-Machacek Model
hep-ph 2025-06 conditional novelty 6.0 of 10

A global fit of the Georgi-Machacek and extended Georgi-Machacek models finds that the 95 GeV diphoton and bottom-quark excesses are compatible with the 125 GeV Higgs data, while the ditau excess is not, and it sets u...
$B\to\pi\ell\ell$ form factors for new-physics searches from lattice QCD
hep-ph 2015-07 conditional novelty 6.0 of 10

Lattice QCD supplies the tensor form factor for B to pi lepton pairs, giving a Standard Model branching ratio of 20.4(2.1) x 10^-9 that agrees with the LHCb measurement.
Differential branching fraction and angular analysis of $\Lambda^{0}_{b} \rightarrow \Lambda \mu^+\mu^-$ decays
hep-ex 2015-03 conditional novelty 6.0 of 10

LHCb measures the differential branching fraction of Lambda_b to Lambda mu+ mu- and reports the first forward-backward asymmetries in the dimuon and proton-pion systems, finding A_FB^h = -0.29 +/- 0.07 +/- 0.03 in 15 ...
Calculation of $B^0 \to K^{*0} \mu^+ \mu^-$ and $B_s^0 \to \phi \mu^+ \mu^-$ observables using form factors from lattice QCD
hep-ph 2013-10 accept novelty 6.0 of 10

Using unquenched lattice QCD form factors, the authors find the Standard Model overpredicts high-q² B → K* μμ and Bs → φ μμ rates by about 30%, and a fit to C9 and C9' yields a 2σ hint of new physics.
Lattice QCD calculation of form factors describing the rare decays $B \to K^* \ell^+ \ell^-$ and $B_s \to \phi \ell^+ \ell^-$
hep-lat 2013-10 accept novelty 6.0 of 10

Full-QCD lattice calculations with 2+1 dynamical quark flavors and NRQCD bottom quarks determine the B to K* and Bs to phi form factors at low recoil with roughly 5 percent total systematic uncertainty.
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.
Symmetries and Asymmetries of B -> K* mu+ mu- Decays in the Standard Model and Beyond
hep-ph 2008-11 accept novelty 6.0 of 10

A complete basis of CP-averaged and CP-violating angular observables for B -> K* mu+ mu- is defined, computed in the Standard Model with full form factors, and shown to discriminate among new-physics scenarios.
CP Asymmetries in bar B -> bar K* (-> bar K pi) l+ l- and Untagged bar B_s,B_s -> phi (-> K+ K-) l+ l- Decays at NLO
hep-ph 2008-05 accept novelty 6.0 of 10

Seven angular CP asymmetries in B -> K* l+ l- are computed at NLO in QCD factorization; all sit at or below the percent level in the Standard Model, while the three T-odd ones can reach order one with new physics.
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.
Anomalous Dimension Matrix for Radiative and Rare Semileptonic B Decays up to Three Loops
hep-ph 2003-06 accept novelty 6.0 of 10

The three-loop mixing of four-quark operators into the semileptonic operators Q9 and Q10 is computed, supplying a missing ingredient for next-to-next-to-leading-order predictions of B to Xs lepton-pair decays.
The Higgs boson decay $h \to bs$ in the Generational Three-Higgs-Doublet Model
hep-ph 2026-08 conditional novelty 5.0 of 10

In the Generational Three-Higgs-Doublet Model, the flavor-changing decay h→bs can reach a branching ratio around 10^-3, dominated by a tree-level Higgs flavor-changing coupling, while surviving current constraints.
Constraining top-quark couplings combining top-quark and $\boldsymbol{B}$ decay observables
hep-ph 2019-09 accept novelty 5.0 of 10

A joint fit of top-quark and B-physics measurements within SMEFT resolves a two-fold ambiguity in the photon-dipole Wilson coefficient and shrinks the allowed 90% regions by up to an order of magnitude, with no signif...
$B\to Kl^+l^-$ decay form factors from three-flavor lattice QCD
hep-lat 2015-09 conditional novelty 5.0 of 10

Lattice QCD with 2+1 flavors yields f+, f0, and fT for B to K l+ l- across the full q2 range, with total errors of about 3% at high q2 and 10-30% at q2 = 0.
Lepton flavor non-universality in $b \to s \ell^+ \ell^-$ processes
hep-ph 2015-03 conditional novelty 5.0 of 10

A lepton-specific right-handed coupling fit to B_s to mu mu and B to K mu mu data predicts R_K* = 1.11(8) and R_K*/R_K = 1.27(19), testable at LHCb.
Physical Constraints on a Class of Two-Higgs Doublet Models with FCNC at tree level
hep-ph 2014-01 conditional novelty 5.0 of 10

A global fit of 36 BGL-type two-Higgs-doublet models to flavour and electroweak data leaves several variants with new scalars light enough for the next LHC run to find.
Model independent constraints on leptoquarks from b -> s l+ l- processes
hep-ph 2012-06 conditional novelty 5.0 of 10

Leptoquark contributions to b to s l+ l- are classified and bounded: only baryon-number-violating vector states generate scalar operators, and the resulting Wilson coefficients are constrained to be of order one or less.
Complementarity of the constraints on New Physics from B_s -> mu+ mu- and from B -> K l+l- decays
hep-ph 2012-05 conditional novelty 5.0 of 10

Combining the B_s -> mu+mu- bound with the measured B -> K l+l- rate yields joint, phase-sensitive constraints on new-physics Wilson coefficients, with |C_S| < 0.7, |C_P| < 1.0, and 2.2 < sqrt(|C10|^2+|C'10|^2) < 4.8.
Model-independent constraints on new physics in b --> s transitions
hep-ph 2011-11 conditional novelty 5.0 of 10

Combining all available b to s rare-decay data, the fit finds every 95% confidence region compatible with the Standard Model, excludes several sign-flipped Wilson coefficient scenarios, and caps Bs to mu mu at roughly...
On transverse asymmetries in B --> K* l+l-
hep-ph 2011-06 accept novelty 5.0 of 10

A new transverse asymmetry A_T^(re) is defined for B to K* l+ l-, and the zero-crossing patterns of three independent asymmetries are shown to discriminate among new-physics scenarios in C7, C9, and C10.
Explaining the $B \to K\mu^+\mu^-$ Anomaly in the Left-Right Inverse Seesaw Model
hep-ph 2026-05 unverdicted novelty 4.0 of 10

The LRIS model explains the B→Kμμ anomaly with ΔC9 ≈ -1 and ΔC10 ≈ 0 through a non-decoupling box diagram while suppressing Bs mixing via GIM-like phases and satisfying constraints.
Revisiting $B\to K^{(\ast)} \nu \bar{\nu}$ decays in the Standard Model and beyond
hep-ph 2023-01 accept novelty 4.0 of 10

Combining B → K(*) νν̄ with B → K(*) ℓℓ in the same low-q² bin gives a ratio whose Standard Model value is predicted to sub-percent precision for the kaon mode and which can be inverted to extract C9^eff from data.
Weak Radiative Decays of the B Meson and Bounds on $M_{H^\pm}$ in the Two-Higgs-Doublet Model
hep-ph 2017-02 accept novelty 4.0 of 10

Updated Belle data on inclusive b to s gamma imply a 95% C.L. lower bound on the charged Higgs mass in 2HDM Model-II between 570 and 800 GeV, with the spread traced to cutoff and confidence-interval choices.
Predictions of selected flavour observables within the Standard Model
hep-ph 2011-06 conditional novelty 4.0 of 10

Using a global fit to CKM inputs, the CKMfitter group predicts branching ratios and CP observables for rare B, D, and K decays, finding 2.7σ and 2.8σ tensions in sin(2β) and B→τν.
The Two Higgs Doublet of Type II facing flavour physics data
hep-ph 2009-07 conditional novelty 4.0 of 10

Combining leptonic, semileptonic and loop flavour observables in a CKMfitter global fit, the Type II two-Higgs-doublet model does not beat the Standard Model and requires a charged Higgs heavier than 316 GeV at 95% CL.
Constraining the Two-Higgs-Doublet-Model parameter space
hep-ph 2007-06 conditional novelty 4.0 of 10

Combining B-physics, LEP electroweak, and tree-level unitarity constraints leaves only a narrow window in the Two-Higgs-Doublet Model's tan beta versus charged-Higgs-mass plane.
Theory and phenomenology of two-Higgs-doublet models
hep-ph 2011-05 accept novelty 3.0 of 10

The review organizes the theory and phenomenology of two-Higgs-doublet models, including flavour-safe variants, charged-scalar searches, vacuum stability, and minimal spontaneous CP-violation constructions.
Climbing NLO and NNLO Summits of Weak Decays: 1988-2023
hep-ph 2011-02 accept novelty 2.0 of 10

A 35-year chronicle of next-to-leading and next-to-next-to-leading order QCD corrections to weak decays, with reference tables, an eight-class taxonomy of correction structures, and personal anecdotes.

How later papers used it

56 later papers cite it

Evidence: substantial. 54 of the citing papers share no author with it, and 8 of those carry a confident label from Pith's citation classifier.

Pith read 15 of the 74 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

2 later papers by other authors are listed below: 2 used its method or tool.

Uses its method or tool 2 of 6 papers with this label

Included the effects of the relevant matrix elements by defining effective Wilson coefficients as in this paper.

New Physics in Gamma_12^s: (sbar b) (taubar tau) Operators (2011) · 0.87 · paraphrased: the licence does not allow quoting
Wrote the Wilson coefficients for new physics at the bottom quark scale as in this paper.

The Higgs boson decay $h \rightarrow bs$ in the NB-LSSM (2026) · 0.81 · paraphrased: the licence does not allow quoting

How the literature uses it

55 arXiv papers cite this in 73 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 · 50 sentences without a confident label

Uses its method or tool 6 papers

We will use the next–to–leading order logarithmic approximation for the Wilson coefficients $C_i^eff$ and $C^new_i$ [ref] at the scale $μ=m_b=4.8 GeV$.

Analysis of Various Polarization Asymmetries In The Inclusive $b\to s \ell^+ \ell^-$ Decay In The Fourth-Generation Standard Model · Numerical analysis · 0.99
The rate is determined from an expansion of the relevant Wilson coefficients in powers of $α_s/(4π)$, starting with (1) the matching of these coefficients to the full theory at some high scale ($μ_0∼m_W$ or $m_t$), then (2) evolving them down to the low scale $μ_b∼m_b$ (in this process the operators mix), and (3) determine the matrix elements at the low scale [ref] .

Dark matter in three-Higgs-doublet models with $S_3$ symmetry · $B$ physics constraints · 0.92
Following common practice, we include the effects of the relevant matrix elements by defining so-called effective Wilson coefficients [ref] .

New Physics in Gamma_12^s: (sbar b) (taubar tau) Operators · Indirect Bounds on $(s̅ b) (τ̅τ)$ Operators · 0.87

Uses its data or values 2 papers

where $C_7γ^(0)eff(m_b)=-0.310$ [ref] , $G_F = (1.166 ×10^-5) GeV^-2$ and the fine structure constant is $α_em≡e^2/4π=1/137$.

Re-analysis of rare radiative $\Xi_b^-\rightarrow \Xi^- \gamma$ decay in QCD · Form factors for the $Ξ_b^-→Ξ^- γ$ decay in light cone QCD sum rules · 1.00
Also the limits on the rare $b→s γ$ decay [ref] following [ref] have been imposed.

Direct Search for Dark Matter - Striking the Balance - and the Future · Cross sections in the effective low-energy MSSM · 0.80

Cites it as background 14 papers

At hadronic energy scales, $b→sγ$ and $b→s ℓ^+ℓ^-$ transitions can be described using an effective Hamiltonian of the form [ref]

Calculation of $B^0 \to K^{*0} \mu^+ \mu^-$ and $B_s^0 \to \phi \mu^+ \mu^-$ observables using form factors from lattice QCD · Introduction · 0.93
The contributions from the four-quark operators $𝒪_1-6$ are included in the redefinition of the coefficients $C_7,9$ [ref] .

Revisiting $B\to K^{(\ast)} \nu \bar{\nu}$ decays in the Standard Model and beyond · $(ν/ℓ)$ ratios · 0.82
Thus eight and a half years after the outline of the NLO $B→X_sγ$ program [ref] , Mikolaj and me could summarize the result of these efforts in the volume of Acta Physica Polonica dedicated to Stefan's 60th birthday [ref] .

Climbing NLO and NNLO Summits of Weak Decays: 1988-2023 · Matrix Elements · 0.81

Discussion

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