Abstract
The LHCb collaboration has recently reported the first observation of CP violation in the penguin-dominated \( {B}_s^0 \) → K−K+ decay and further new measurements, indicating differences between the direct CP asymmetries of both the \( {B}_s^0 \) → K−K+, \( {B}_d^0 \) → π−K+ and the \( {B}_d^0 \) → π−π+, \( {B}_s^0 \) → K−π+ modes. We show that these puzzling differences can be accommodated through sizeable penguin annihilation and exchange topologies in the Standard Model, and constrain them. Utilising the U-spin symmetry, we extract the angle γ of the unitarity triangle from the CP asymmetries in the \( {B}_s^0 \) → K−K+, \( {B}_d^0 \) → π−π+ system alone, finding \( \gamma =\left({65}_{-7}^{+11}\right){}^{\circ} \), in perfect agreement with the determination from tree-level B → DK decays. The \( {B}_s^0-{\overline{B}}_s^0 \) mixing phase ϕs can be extracted from CP violation measurements in \( {B}_s^0 \) → K−K+ in a clean way. We present a new strategy and extract ϕs = −(3.6 ± 5.4)°. This result is in agreement with the determination from \( {B}_s^0 \) → J/ψϕ decays. New CP-violating contributions would influence these determinations differently. Hence it is interesting to keep monitoring both as the experimental picture sharpens.
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M. Gronau, O.F. Hernandez, D. London and J.L. Rosner, Broken SU(3) symmetry in two-body B decays, Phys. Rev. D 52 (1995) 6356 [hep-ph/9504326] [INSPIRE].
M. Neubert and J.L. Rosner, New bound on gamma from B+ → πK decays, Phys. Lett. B 441 (1998) 403 [hep-ph/9808493] [INSPIRE].
R. Fleischer, New strategies to extract beta and gamma from Bd → π+π− and BS → K+K−, Phys. Lett. B 459 (1999) 306 [hep-ph/9903456] [INSPIRE].
A.J. Buras and R. Fleischer, A general analysis of gamma determinations from B → πK decays, Eur. Phys. J. C 11 (1999) 93 [hep-ph/9810260] [INSPIRE].
R. Fleischer, R. Jaarsma and K.K. Vos, Towards new frontiers with B → πK decays, Phys. Lett. B 785 (2018) 525 [arXiv:1712.02323] [INSPIRE].
R. Fleischer, R. Jaarsma, E. Malami and K.K. Vos, Exploring B → ππ, πK decays at the high-precision frontier, Eur. Phys. J. C 78 (2018) 943 [arXiv:1806.08783] [INSPIRE].
T. Huber and G. Tetlalmatzi-Xolocotzi, Estimating QCD-factorization amplitudes through SU(3) symmetry in B → PP decays, Eur. Phys. J. C 82 (2022) 210 [arXiv:2111.06418] [INSPIRE].
R. Fleischer, Bs,d → ππ, πK, KK: status and prospects, Eur. Phys. J. C 52 (2007) 267 [arXiv:0705.1121] [INSPIRE].
R. Fleischer and R. Knegjens, In pursuit of new physics with \( {B}_s^0 \) → K+K−, Eur. Phys. J. C 71 (2011) 1532 [arXiv:1011.1096] [INSPIRE].
M. Ciuchini, E. Franco, S. Mishima and L. Silvestrini, Testing the Standard Model and searching for new physics with Bd → ππ and Bs → KK decays, JHEP 10 (2012) 029 [arXiv:1205.4948] [INSPIRE].
R. Fleischer, R. Jaarsma and K.K. Vos, Towards new frontiers in the exploration of charmless non-leptonic B decays, JHEP 03 (2017) 055 [arXiv:1612.07342] [INSPIRE].
R. Fleischer, R. Jaarsma and K.K. Vos, New strategy to explore CP violation with \( {B}_s^0 \) → K−K+, Phys. Rev. D 94 (2016) 113014 [arXiv:1608.00901] [INSPIRE].
Y. Nir, I. Savoray and Y. Viernik, Lessons from the LHCb measurement of CP violation in Bs → K+K−, JHEP 07 (2022) 068 [arXiv:2201.03573] [INSPIRE].
LHCb collaboration, Observation of CP violation in two-body \( {B}_{(s)}^0 \)-meson decays to charged pions and kaons, JHEP 03 (2021) 075 [arXiv:2012.05319] [INSPIRE].
M. Beneke, G. Buchalla, M. Neubert and C.T. Sachrajda, QCD factorization for B → ππ decays: strong phases and CP violation in the heavy quark limit, Phys. Rev. Lett. 83 (1999) 1914 [hep-ph/9905312] [INSPIRE].
M. Beneke, G. Buchalla, M. Neubert and C.T. Sachrajda, QCD factorization in B → πK, ππ decays and extraction of Wolfenstein parameters, Nucl. Phys. B 606 (2001) 245 [hep-ph/0104110] [INSPIRE].
C. Bobeth, M. Gorbahn and S. Vickers, Weak annihilation and new physics in charmless B → MM decays, Eur. Phys. J. C 75 (2015) 340 [arXiv:1409.3252] [INSPIRE].
M. Gavrilova, Y. Grossman and S. Schacht, The mathematical structure of U-spin amplitude sum rules, JHEP 08 (2022) 278 [arXiv:2205.12975] [INSPIRE].
S. Faller, R. Fleischer and T. Mannel, Precision physics with \( {B}_s^0 \) → J/ψϕ at the LHC: the quest for new physics, Phys. Rev. D 79 (2009) 014005 [arXiv:0810.4248] [INSPIRE].
K. De Bruyn and R. Fleischer, A roadmap to control penguin effects in \( {B}_d^0\to J/\psi {K}_s^0 \) and \( {B}_s^0 \) → J/ψϕ, JHEP 03 (2015) 145 [arXiv:1412.6834] [INSPIRE].
M.Z. Barel, K. De Bruyn, R. Fleischer and E. Malami, In pursuit of new physics with \( {B}_d^0 \) → J/ψK0 and \( {B}_s^0 \) → J/ψϕ decays at the high-precision frontier, J. Phys. G 48 (2021) 065002 [arXiv:2010.14423] [INSPIRE].
M.Z. Barel, K. De Bruyn, R. Fleischer and E. Malami, Penguin effects in \( {B}_d^0\to J/\psi {K}_s^0 \) and \( {B}_s^0 \) → J/ψϕ, in 11th international workshop on the CKM unitarity triangle, (2022) [arXiv:2203.14652] [INSPIRE].
L. Wolfenstein, Parametrization of the Kobayashi-Maskawa matrix, Phys. Rev. Lett. 51 (1983) 1945 [INSPIRE].
A.J. Buras, M.E. Lautenbacher and G. Ostermaier, Waiting for the top quark mass, K+ → π+\( \nu \overline{\nu} \), \( {B}_s^0 \)-\( {\overline{B}}_s^0 \) mixing and CP asymmetries in B decays, Phys. Rev. D 50 (1994) 3433 [hep-ph/9403384] [INSPIRE].
R. Fleischer, CP violation in the B system and relations to K → \( \pi \nu \overline{\nu} \) decays, Phys. Rept. 370 (2002) 537 [hep-ph/0207108] [INSPIRE].
LHCb collaboration, Measurement of CP asymmetries in two-body \( {B}_{(s)}^0 \)-meson decays to charged pions and kaons, Phys. Rev. D 98 (2018) 032004 [arXiv:1805.06759] [INSPIRE].
K. De Bruyn, R. Fleischer, E. Malami and P. van Vliet, New physics in \( {B}_q^0-{\overline{B}}_q^0 \) mixing: present challenges, prospects, and implications for \( {B}_q^0 \) → μ+μ−, Tech. Rep. Nikhef-2022-012 (2022) [arXiv:2208.14910] [INSPIRE].
K. De Bruyn, R. Fleischer, R. Knegjens, P. Koppenburg, M. Merk and N. Tuning, Branching ratio measurements of Bs decays, Phys. Rev. D 86 (2012) 014027 [arXiv:1204.1735] [INSPIRE].
HFLAV collaboration, Averages of b-hadron, c-hadron, and τ-lepton properties as of 2021, arXiv:2206.07501 [INSPIRE].
LHCb collaboration, First measurement of time-dependent CP violation in \( {B}_s^0 \) → K+K− decays, JHEP 10 (2013) 183 [arXiv:1308.1428] [INSPIRE].
LHCb collaboration, Determination of γ and −2βs from charmless two-body decays of beauty mesons, Phys. Lett. B 741 (2015) 1 [arXiv:1408.4368] [INSPIRE].
LHCb collaboration, Simultaneous determination of CKM angle γ and charm mixing parameters, JHEP 12 (2021) 141 [arXiv:2110.02350] [INSPIRE].
Particle Data Group collaboration, Review of particle physics, PTEP 2022 (2022) 083C01 [INSPIRE].
LHCb collaboration, First observation of the decay \( {B}_s^0 \) → K−μ+νμ and measurement of |Vub|/|Vcb|, Phys. Rev. Lett. 126 (2021) 081804 [arXiv:2012.05143] [INSPIRE].
J.L. Rosner, S. Stone and R.S. Van de Water, Leptonic decays of charged pseudoscalar mesons — 2015, Tech. Rep. EFI-15-21 (2015) [arXiv:1509.02220] [INSPIRE].
A. Khodjamirian and A.V. Rusov, Bs → Kℓνℓ and B(s) → π(K)ℓ+ℓ− decays at large recoil and CKM matrix elements, JHEP 08 (2017) 112 [arXiv:1703.04765] [INSPIRE].
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Fleischer, R., Jaarsma, R. & Vos, K.K. Zooming into CP violation in B(s) → hh decays. J. High Energ. Phys. 2023, 81 (2023). https://doi.org/10.1007/JHEP02(2023)081
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DOI: https://doi.org/10.1007/JHEP02(2023)081