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arxiv: 2605.22088 · v1 · pith:VU6X6HNWnew · submitted 2026-05-21 · ✦ hep-ph · hep-ex

bto c bar u q decay and CP violating observables in the presence of new physics contributions

Xuanning Guo , Albertus Hariwangsa Panuluh , Hiroyuki Umeeda , Jinglong Zhu This is my paper

Pith reviewed 2026-05-22 05:40 UTC · model grok-4.3

classification ✦ hep-ph hep-ex
keywords b to c u q transitionsnew physicsWilson coefficientsCP asymmetryB meson decaysbranching fractionsDelta GammaA_SL
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0 comments X

The pith

New physics contributions to b to c u-bar q transitions resolve branching fraction tensions and produce correlated predictions for CP asymmetries and B meson width differences.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper carries out a comprehensive study of b to c u-bar q decays with possible new physics included. It begins from the observed mismatch between experimental branching fractions for B and Bs decays to D and Ds mesons and the results of QCD factorization calculations. Complex-valued Wilson coefficients are introduced in the effective Hamiltonian and constrained using data on direct CP asymmetry in B minus to D zero pi minus, the CKM angle gamma, lifetime ratios, and mixing parameters such as Delta Gamma over Gamma and A_SL. The resulting bounds in color-singlet and color-rearranged scenarios then generate linked predictions among several observables. A reader would care because these links offer multiple independent tests of whether a single new physics source can explain several B decay discrepancies at once.

Core claim

By positing new physics contributions to the Wilson coefficients of the effective Hamiltonian for b to c u-bar q transitions, the tensions between measured and calculated branching fractions for B(s) to D(s)(*) M decays can be accommodated, yielding 1 sigma and 2 sigma constraints on the complex coefficients that imply specific correlations among Delta Gamma_d over Gamma_d, A_SL^d, and the direct CP asymmetry A_CP.

What carries the argument

Complex-valued new physics Wilson coefficients added to the effective Hamiltonian for b to c u-bar q transitions, which modify the decay amplitudes in color-singlet and color-rearranged operator scenarios to fit branching fractions while generating predictions for CP-violating and mixing observables.

If this is right

  • The complex Wilson coefficients receive 1 sigma and 2 sigma bounds in both the color-singlet and color-rearranged cases.
  • These bounds produce explicit numerical correlations linking Delta Gamma_d over Gamma_d, A_SL^d, and A_CP.
  • The same coefficients also affect the extraction of the CKM angle gamma when combined with lifetime ratio data.
  • The approach simultaneously addresses multiple B decay rate discrepancies through a shared set of parameters.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the same operators contribute elsewhere, similar new physics effects could appear in other b to c transitions not studied in this work.
  • Future precision data from LHCb or Belle II on the predicted correlations could confirm or exclude the scenario.
  • The framework might connect to other flavor observables if the Wilson coefficients overlap with those appearing in different decay channels.

Load-bearing premise

The observed tensions between experimental branching fractions for B(s) to D(s)(*) M decays and QCD factorization results arise from new physics in the b to c u-bar q Wilson coefficients rather than from shortcomings in the QCD calculations.

What would settle it

A high-precision measurement of the direct CP asymmetry in B minus to D zero pi minus that falls outside the range correlated with the measured Delta Gamma_d over Gamma_d under the constrained Wilson coefficients would rule out this new physics scenario.

Figures

Figures reproduced from arXiv: 2605.22088 by Albertus Hariwangsa Panuluh, Hiroyuki Umeeda, Jinglong Zhu, Xuanning Guo.

Figure 1
Figure 1. Figure 1: FIG. 1: Topological diagrams contributing to [PITH_FULL_IMAGE:figures/full_fig_p012_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: The reference decay channel [PITH_FULL_IMAGE:figures/full_fig_p013_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Combined constraints on the NP Wilson coefficient [PITH_FULL_IMAGE:figures/full_fig_p016_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Combined constraints on the NP Wilson coefficient [PITH_FULL_IMAGE:figures/full_fig_p017_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Combined constraints on the NP Wilson coefficients [PITH_FULL_IMAGE:figures/full_fig_p017_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Combined constraints on the NP Wilson coefficients [PITH_FULL_IMAGE:figures/full_fig_p018_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: (and also in Figs. 8 and 9 discussed later), predicted regions of the observables are significantly reduced if the constraint from γ is considered additionally. FIG. 7: The predicted regions in the (∆Γd/Γd, Ad SL) plane for the baseline scenario where C NP 1 = 0 (i.e., NP only enters via C NP 2 ). The blue and grey error bars represent the current experimental constraints [40, 43] and the SM predictions [2… view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: The predicted regions in the ( [PITH_FULL_IMAGE:figures/full_fig_p021_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: The predicted regions in the ( [PITH_FULL_IMAGE:figures/full_fig_p022_9.png] view at source ↗
read the original abstract

In this work, a comprehensive analysis for processes related to $b\to c\bar{u}q~(q=d, s)$ transitions are carried out, including new physics contributions. In light of a recent tension between branching fractions for $B_{(s)}\to D_{(s)}^{(*)}M$ ($M$ represents a meson) decays in the QCD factorization approach and relevant experimental results, phenomenological constraints on complex-valued Wilson coeffients are discussed. Analyzed observables contain direct CP asymmetry ($A_{\text{CP}}$) in $B^-\to D^0\pi^-$ decays and $\gamma/\phi_3$, one of the angles in the unitarity triangle, combined with others from $\tau_{B^+}/\tau_{B_d}$, $\Delta\Gamma_{q}/\Gamma_q$, and $A_{\rm SL}^{q}~(q=d, s)$. We constrain the complex Wilson coefficients at $1\sigma$ and $2\sigma$ levels under color-singlet and color-rearranged scenarios. These constraints yield correlated predictions for $\Delta\Gamma_d/\Gamma_d$, $A_{\rm SL}^d$ and $A_{\text{CP}}$.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript presents a phenomenological analysis of b → c ū q (q=d,s) transitions including new physics contributions to the Wilson coefficients of the effective Hamiltonian. Motivated by tensions between experimental branching fractions for B_{(s)} → D_{(s)}^{(*)} M decays and QCD factorization predictions, the authors constrain complex-valued Wilson coefficients C1 and C2 under color-singlet and color-rearranged scenarios. These constraints are then used to derive correlated predictions for observables including direct CP asymmetry A_CP in B^- → D^0 π^-, the CKM angle γ/φ3, lifetime ratios τ_{B^+}/τ_{B_d}, ΔΓ_q/Γ_q, and A_SL^q (q=d,s).

Significance. If the assumption that the branching-fraction tensions are dominantly due to new physics holds, the work provides a framework for linking several CP-violating and mixing observables through a common set of Wilson coefficients, yielding testable predictions for ΔΓ_d/Γ_d, A_SL^d and A_CP that could be confronted with future data from LHCb and Belle II. The approach is relevant to the broader program of searching for new physics in non-leptonic b decays.

major comments (2)
  1. The central claim rests on the premise that the observed discrepancies between measured branching fractions and QCD factorization calculations for B(s)→D(s)(*)M decays are primarily attributable to new physics in the b→cūq Wilson coefficients rather than to hadronic uncertainties. The manuscript does not quantify the expected magnitude of O(α_s^2) corrections, power-suppressed terms, or final-state interactions relative to the size of the tension; this justification is load-bearing for the 1σ/2σ bounds and the subsequent correlated predictions.
  2. The predictions for ΔΓ_d/Γ_d, A_SL^d and A_CP are derived from Wilson coefficients fitted to the same class of branching-fraction data that motivated the analysis. This creates a potential circularity in which the reported predictions largely reflect the input constraints rather than constituting independent tests; a clearer separation of fit inputs from predicted observables or the inclusion of additional independent data would be required to substantiate the claim of correlated predictions.
minor comments (2)
  1. The definitions of the color-singlet and color-rearranged scenarios for the Wilson coefficients should be stated explicitly, with reference to the standard operator basis, to avoid ambiguity in the effective Hamiltonian.
  2. A summary table listing the 1σ and 2σ allowed ranges for the complex Wilson coefficients in both scenarios would improve readability and allow direct comparison with future experimental updates.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed review and valuable comments on our manuscript. We have carefully considered the major comments and provide point-by-point responses below. We agree that additional clarification is needed regarding the assumptions and the nature of the predictions, and we will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: The central claim rests on the premise that the observed discrepancies between measured branching fractions and QCD factorization calculations for B(s)→D(s)(*)M decays are primarily attributable to new physics in the b→cūq Wilson coefficients rather than to hadronic uncertainties. The manuscript does not quantify the expected magnitude of O(α_s^2) corrections, power-suppressed terms, or final-state interactions relative to the size of the tension; this justification is load-bearing for the 1σ/2σ bounds and the subsequent correlated predictions.

    Authors: We acknowledge the importance of this point. Our analysis is predicated on exploring the new physics hypothesis to explain the reported tensions in the branching fractions, as stated in the introduction. The QCD factorization framework used in the literature already incorporates estimates of theoretical uncertainties, and the tensions are presented as exceeding these. However, we agree that a more explicit discussion of the expected size of higher-order corrections would strengthen the justification. In the revised manuscript, we will add a paragraph in Section 2 or the introduction quantifying or referencing the expected magnitudes of O(α_s²) and power corrections from existing literature, and discuss how they compare to the observed tensions. revision: yes

  2. Referee: The predictions for ΔΓ_d/Γ_d, A_SL^d and A_CP are derived from Wilson coefficients fitted to the same class of branching-fraction data that motivated the analysis. This creates a potential circularity in which the reported predictions largely reflect the input constraints rather than constituting independent tests; a clearer separation of fit inputs from predicted observables or the inclusion of additional independent data would be required to substantiate the claim of correlated predictions.

    Authors: We appreciate this observation on potential circularity. The branching fraction measurements serve as inputs to constrain the Wilson coefficients C1 and C2. The other observables, such as the lifetime ratio, ΔΓ_q/Γ_q, A_SL^q, and A_CP, are computed as predictions from these constrained coefficients. While they are correlated by construction, they represent distinct experimental measurements that can provide independent tests of the NP scenario. For example, a measurement of A_CP in B^- → D^0 π^- can be compared directly to our prediction. To clarify this, we will revise the manuscript to explicitly list the input observables used in the fit and separate them from the predicted ones, perhaps in a dedicated subsection or table. We will also emphasize that these correlations allow for future consistency checks with data from LHCb and Belle II. revision: yes

Circularity Check

1 steps flagged

Wilson coefficients fitted to branching-fraction tensions are used to generate correlated 'predictions' for ΔΓ_d/Γ_d, A_SL^d and A_CP

specific steps
  1. fitted input called prediction [Abstract]
    "In light of a recent tension between branching fractions for B_{(s)}→D_{(s)}^{(*)}M (M represents a meson) decays in the QCD factorization approach and relevant experimental results, phenomenological constraints on complex-valued Wilson coeffients are discussed. ... These constraints yield correlated predictions for ΔΓ_d/Γ_d, A_SL^d and A_CP."

    The constraints are obtained by fitting the Wilson coefficients directly to the branching-fraction data that exhibit the tension; the subsequent 'predictions' for ΔΓ_d/Γ_d, A_SL^d and A_CP are therefore computed from the same fitted parameters and do not constitute independent tests.

full rationale

The paper takes the observed discrepancy between measured B(s)→D(s)(*)M branching fractions and QCDF predictions as the primary input, fits complex Wilson coefficients C1 and C2 to that discrepancy under two scenarios, and then presents the resulting values as yielding predictions for lifetime ratios, semileptonic asymmetries and direct CP asymmetries. Because the target observables are not independent of the fitted data set but are instead linear combinations or related matrix elements evaluated at the same fitted points, the 'predictions' reduce to re-expressions of the input fit. No external benchmark or unfitted observable is used to validate the chain, producing partial circularity of the fitted-input-called-prediction type.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on fitting complex Wilson coefficients to resolve tensions between QCD factorization calculations and experimental branching fractions; no independent evidence is provided for the new physics contributions beyond the fit itself.

free parameters (1)
  • complex Wilson coefficients
    Fitted to branching fraction data for B_{(s)}→D_{(s)}^{(*)}M decays under color-singlet and color-rearranged scenarios.
axioms (1)
  • domain assumption QCD factorization approach accurately computes the branching fractions in the absence of new physics
    Invoked to identify tensions with experiment that motivate the new physics analysis.

pith-pipeline@v0.9.0 · 5754 in / 1292 out tokens · 36700 ms · 2026-05-22T05:40:20.797989+00:00 · methodology

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Works this paper leans on

61 extracted references · 61 canonical work pages · 25 internal anchors

  1. [1]

    The mass difference M q 21 remains dominated 7 by the SM top-quark loops and is unaffected by the NP considered here. Consequently, the constraints from Bq − ¯Bq mixing observables can be derived as: ∆Γq|exp = −2 |M q 21| Re Γq 21,SM + Γq 21,NP M q 21 = ∆Γ q,SM − 2 |M q 21| Re Γq 21,NP M q 21 , Aq SL|exp = −Im Γq 21,SM + Γq 21,NP M q 21 = Aq SL,SM − Im Γq...

    work page 2025

  2. [2]

    [ 56]: Oq 1 = (¯biqi)V −A(¯bjqj)V −A, Oq 2 = (¯biqi)S−P (¯bjqj)S−P Oq 3 = (¯biqj)S−P (¯bjqi)S−P , Oq 4 = (¯biqi)S−P (¯bjqj)S+P , Oq 5 = (¯biqj)S−P (¯bjqi)S+P

    Effective Operator Basis For the analysis of B meson mixing, we employ the complete operator basis introduced in Ref. [ 56]: Oq 1 = (¯biqi)V −A(¯bjqj)V −A, Oq 2 = (¯biqi)S−P (¯bjqj)S−P Oq 3 = (¯biqj)S−P (¯bjqi)S−P , Oq 4 = (¯biqi)S−P (¯bjqj)S+P , Oq 5 = (¯biqj)S−P (¯bjqi)S+P . (B1) The hadronic matrix elements are parametrized in terms of bag parameters a...

    work page

  3. [3]

    Analytical Expressions for the Mixing Coefficients Adopting the formalism from Ref. [ 38], the general expressions for the coefficient functions Dk are decomposed into current-current ( F ) and penguin-like ( P ) contributions: Duu k (µ2) = X i,j=1,2 C ∗ i (µ1)C ∗ j (µ1)F uu k,ij(µ1, µ2) + αs 4π (C ∗ 2 (µ1))2P uu k,22(µ1, µ2) + 2 αs 4π C ∗ 2 C ∗ 8GP u k,28 ...

    work page

  4. [4]

    QCD factorization for exclusive, non-leptonic B meson decays: General arguments and the case of heavy-light final states

    M. Beneke, G. Buchalla, M. Neubert, and C. T. Sachrajda, Nucl. Phys. B 591, 313 (2000) , arXiv:hep-ph/0006124

    work page internal anchor Pith review Pith/arXiv arXiv 2000

  5. [5]

    Two-body non-leptonic heavy-to-heavy decays at NNLO in QCD factorization

    T. Huber, S. Kränkl, and X.-Q. Li, JHEP 09, 112 , arXiv:1606.02888 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv

  6. [6]

    Bordone, N

    M. Bordone, N. Gubernari, T. Huber, M. Jung, and D. van Dyk, Eur. Phys. J. C 80, 951 (2020), arXiv:2007.10338 [hep-ph]

    work page arXiv 2020

  7. [7]

    M. L. Piscopo and A. V. Rusov, JHEP 10, 180 , arXiv:2307.07594 [hep-ph]

    work page arXiv

  8. [8]

    M. Endo, S. Iguro, and S. Mishima, JHEP 01, 147 , arXiv:2109.10811 [hep-ph]

    work page arXiv

  9. [9]

    Chua, W.-S

    C.-K. Chua, W.-S. Hou, and K.-C. Yang, Phys. Rev. D 65, 096007 (2002) , arXiv:hep- ph/0112148

    work page arXiv 2002

  10. [10]

    Implications of Bbar to D0 h0 Decays on Bbar to D Kbar, Dbar Kbar Decays

    C.-K. Chua and W.-S. Hou, Phys. Rev. D 72, 036002 (2005) , arXiv:hep-ph/0504084

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  11. [11]

    Rescattering effects in B_{u,d,s}(bar) to D P, D(bar) P decays

    C.-K. Chua and W.-S. Hou, Phys. Rev. D 77, 116001 (2008) , arXiv:0712.1882 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  12. [12]

    Revisiting Final State Interaction in Charmless $B_q\to P P$ Decays

    C.-K. Chua, Phys. Rev. D 97, 093004 (2018) , arXiv:1802.00155 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  13. [13]

    Iguro and T

    S. Iguro and T. Kitahara, Phys. Rev. D 102, 071701 (2020) , arXiv:2008.01086 [hep-ph]

    work page arXiv 2020

  14. [14]

    Cai, W.-J

    F.-M. Cai, W.-J. Deng, X.-Q. Li, and Y.-D. Yang, JHEP 10, 235 , arXiv:2103.04138 [hep-ph]

    work page arXiv

  15. [15]

    Fleischer and E

    R. Fleischer and E. Malami, Phys. Rev. D 106, 056004 (2022) , arXiv:2109.04950 [hep-ph]

    work page arXiv 2022

  16. [16]

    A. Lenz, J. Müller, M. L. Piscopo, and A. V. Rusov, JHEP 09, 028, arXiv:2211.02724 [hep-ph]

    work page arXiv

  17. [17]

    A. H. Panuluh, S. Tanaka, and H. Umeeda, Phys. Rev. D 111, 095020 (2025), arXiv:2408.15466 [hep-ph]

    work page arXiv 2025

  18. [18]

    Meiser, D

    S. Meiser, D. van Dyk, and J. Virto, JHEP 06, 019 , arXiv:2411.09458 [hep-ph]

    work page arXiv

  19. [19]

    Phenomenological Study of Heavy Hadron Lifetimes

    H.-Y. Cheng, JHEP 11, 014 , arXiv:1807.00916 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv

  20. [20]

    A. Lenz, M. L. Piscopo, and A. V. Rusov, JHEP 01, 004 , arXiv:2208.02643 [hep-ph]

    work page arXiv

  21. [21]

    Egner, M

    M. Egner, M. Fael, A. Lenz, M. L. Piscopo, A. V. Rusov, K. Schönwald, and M. Steinhauser, JHEP 04, 106 , arXiv:2412.14035 [hep-ph]

    work page arXiv

  22. [22]

    M. Lang, A. Lenz, A. Mohamed, M. L. Piscopo, and A. V. Rusov, arXiv:2512.14635 [hep-ph] (2025)

    work page arXiv 2025

  23. [23]

    Albrecht, F

    J. Albrecht, F. Bernlochner, A. Lenz, and A. Rusov, Eur. Phys. J. ST 233, 359 (2024) , arXiv:2402.04224 [hep-ph]

    work page arXiv 2024

  24. [24]

    Nierste, P

    U. Nierste, P. Reeck, V. Shtabovenko, and M. Steinhauser, JHEP 03, 094 , arXiv:2512.07949 [hep-ph]. 31

    work page arXiv

  25. [25]

    Physics case for an LHCb Upgrade II - Opportunities in flavour physics, and beyond, in the HL-LHC era

    R. Aaij et al. (LHCb), arXiv:1808.08865 [hep-ex] (2018)

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  26. [26]

    Opportunities in Flavour Physics at the HL-LHC and HE-LHC

    A. Cerri et al. , CERN Yellow Rep. Monogr. 7, 867 (2019) , arXiv:1812.07638 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  27. [27]

    J. Brod, A. Lenz, G. Tetlalmatzi-Xolocotzi, and M. Wiebusch, Phys. Rev. D 92, 033002 (2015), arXiv:1412.1446 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  28. [28]

    New Strategies to Obtain Insights into CP Violation Through $B_s\to D_s^{\pm}K^\mp, D_s^{\ast\pm}K^\mp, ...$ and $B_d\to D^{\pm}\pi^\mp, D^{\ast\pm}\pi^\mp, ...$ Decays

    R. Fleischer, Nucl. Phys. B 671, 459 (2003) , arXiv:hep-ph/0304027

    work page internal anchor Pith review Pith/arXiv arXiv 2003

  29. [29]

    Gronau and D

    M. Gronau and D. London, Phys. Lett. B 253, 483 (1991)

    work page 1991

  30. [30]

    Gronau and D

    M. Gronau and D. Wyler, Phys. Lett. B 265, 172 (1991)

    work page 1991

  31. [31]

    Enhanced CP Violation with $B\to K D^0 (\overline D^0)$ Modes and Extraction of the CKM Angle gamma

    D. Atwood, I. Dunietz, and A. Soni, Phys. Rev. Lett. 78, 3257 (1997) , arXiv:hep-ph/9612433

    work page internal anchor Pith review Pith/arXiv arXiv 1997

  32. [32]

    Improved Methods for Observing CP Violation in B+/- --> K+/- D0 and Measuring the CKM Phase gamma

    D. Atwood, I. Dunietz, and A. Soni, Phys. Rev. D 63, 036005 (2001) , arXiv:hep-ph/0008090

    work page internal anchor Pith review Pith/arXiv arXiv 2001

  33. [33]

    Fleischer and E

    R. Fleischer and E. Malami, Eur. Phys. J. C 83, 420 (2023) , arXiv:2110.04240 [hep-ph]

    work page arXiv 2023

  34. [34]

    Aaij et al

    R. Aaij et al. (LHCb), arXiv:2603.10860 [hep-ex] (2026)

    work page arXiv 2026

  35. [35]

    Gershon, A

    T. Gershon, A. Lenz, A. V. Rusov, and N. Skidmore, Phys. Rev. D 105, 115023 (2022) , arXiv:2111.04478 [hep-ph]

    work page arXiv 2022

  36. [36]

    Abe et al

    K. Abe et al. (Belle), Phys. Rev. D 73, 051106 (2006) , arXiv:hep-ex/0601032

    work page arXiv 2006

  37. [37]

    Bloomfield et al

    T. Bloomfield et al. (Belle), Phys. Rev. D 105, 072007 (2022) , arXiv:2111.12337 [hep-ex]

    work page arXiv 2022

  38. [38]

    Adachi et al

    I. Adachi et al. (Belle, Belle-II), JHEP 05, 212 , arXiv:2308.05048 [hep-ex]

    work page arXiv

  39. [39]

    Observation of the suppressed ADS modes $B^\pm \to [\pi^\pm K^\mp \pi^+\pi^-]_D K^\pm$ and $B^\pm \to [\pi^\pm K^\mp \pi^+\pi^-]_D \pi^\pm$

    R. Aaij et al. (LHCb), Phys. Lett. B 723, 44 (2013) , arXiv:1303.4646 [hep-ex]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  40. [40]

    Weak Decays Beyond Leading Logarithms

    G. Buchalla, A. J. Buras, and M. E. Lautenbacher, Rev. Mod. Phys. 68, 1125 (1996) , arXiv:hep-ph/9512380

    work page internal anchor Pith review Pith/arXiv arXiv 1996

  41. [41]

    Ciuchini, E

    M. Ciuchini, E. Franco, V. Lubicz, F. Mescia, and C. Tarantino, JHEP 08, 031 , arXiv:hep- ph/0308029

    work page arXiv

  42. [42]

    Inami and C

    T. Inami and C. S. Lim, Prog. Theor. Phys. 65, 297 (1981) , [Erratum: Prog.Theor.Phys. 65, 1772 (1981)]

    work page 1981

  43. [43]

    Navas et al

    S. Navas et al. (Particle Data Group), Phys. Rev. D 110, 030001 (2024)

    work page 2024

  44. [44]

    Y.-Y. Keum, T. Kurimoto, H. N. Li, C.-D. Lu, and A. I. Sanda, Phys. Rev. D 69, 094018 (2004), arXiv:hep-ph/0305335

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  45. [45]

    HFLA V Collaboration, Summer 2025 updates, https://hflav.web.cern.ch/ (2025), [Ac- cessed: 2026-01-21]

    work page 2025

  46. [46]

    Averages of $b$-hadron, $c$-hadron, and $\tau$-lepton properties as of 2023

    S. Banerjee et al. (Heavy Flavor A veraging Group (HFLA V)), Phys. Rev. D 113, 012008 (2026), arXiv:2411.18639 [hep-ex] . 32

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  47. [47]

    K. G. Chetyrkin, J. H. Kuhn, and M. Steinhauser, Comput. Phys. Commun. 133, 43 (2000) , arXiv:hep-ph/0004189

    work page internal anchor Pith review Pith/arXiv arXiv 2000

  48. [48]

    Measurement of $CP$ asymmetry in $B_s^0 \to D_s^{\mp} K^{\pm}$ decays

    R. Aaij et al. (LHCb), JHEP 03, 059 , arXiv:1712.07428 [hep-ex]

    work page internal anchor Pith review Pith/arXiv arXiv

  49. [49]

    Aaij et al

    R. Aaij et al. (LHCb), JHEP 03, 139 , arXiv:2412.14074 [hep-ex]

    work page arXiv

  50. [50]

    Measurement of Time-Dependent CP-Violating Asymmetries and Constraints on sin(2 beta+gamma) with Partial Reconstruction of B->D*-+pi+- Decays

    B. Aubert et al. (BaBar), Phys. Rev. D 71, 112003 (2005) , arXiv:hep-ex/0504035

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  51. [51]

    F. J. Ronga et al. (Belle), Phys. Rev. D 73, 092003 (2006) , arXiv:hep-ex/0604013

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  52. [52]

    Measurement of time-dependent CP asymmetries in B0->D(*)+-pi-+ and B0->D+-rho-+ decays

    B. Aubert et al. (BaBar), Phys. Rev. D 73, 111101 (2006) , arXiv:hep-ex/0602049

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  53. [53]

    Measurement of $CP$ violation in $B^{0}\rightarrow D^{\mp}\pi^{\pm}$ decays

    R. Aaij et al. (LHCb), JHEP 06, 084 , arXiv:1805.03448 [hep-ex]

    work page internal anchor Pith review Pith/arXiv arXiv

  54. [54]

    FLAG Review 2024

    Y. Aoki et al. (Flavour Lattice A veraging Group (FLAG)), Phys. Rev. D 113, 014508 (2026) , arXiv:2411.04268 [hep-lat]

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  55. [55]

    Black, M

    M. Black, M. Lang, A. Lenz, and Z. Wüthrich, JHEP 04, 081 , arXiv:2412.13270 [hep-ph]

    work page arXiv

  56. [56]

    Bordone, B

    M. Bordone, B. Capdevila, and P. Gambino, Phys. Lett. B 822, 136679 (2021) , arXiv:2107.00604 [hep-ph]

    work page arXiv 2021

  57. [57]

    C. T. H. Davies, J. Harrison, G. P. Lepage, C. J. Monahan, J. Shigemitsu, and M. Wingate (HPQCD), Phys. Rev. Lett. 124, 082001 (2020) , arXiv:1910.00970 [hep-lat]

    work page arXiv 2020

  58. [58]

    Di Luzio, M

    L. Di Luzio, M. Kirk, A. Lenz, and T. Rauh, JHEP 12, 009 , arXiv:1909.11087 [hep-ph]

    work page arXiv 1909

  59. [59]

    B-parameters of the complete set of matrix elements of (Delta B = 2) operators from the lattice

    D. Becirevic, V. Gimenez, G. Martinelli, M. Papinutto, and J. Reyes, JHEP 04, 025 , arXiv:hep-lat/0110091

    work page internal anchor Pith review Pith/arXiv arXiv

  60. [60]

    Branching Ratios of $B \to D_s K$ Decays in Perturbative QCD Approach

    C.-D. Lu and K. Ukai, Eur. Phys. J. C 28, 305 (2003) , arXiv:hep-ph/0210206

    work page internal anchor Pith review Pith/arXiv arXiv 2003

  61. [61]

    Y. Y. Keum, H.-N. Li, and A. I. Sanda, Phys. Rev. D 63, 054008 (2001) , arXiv:hep- ph/0004173. 33

    work page arXiv 2001