Abstract
The decay KS → (μ+μ−)ℓ=0, with the final muon pair in an angular-momentum zero state, is a sensitive probe of short-distance physics. It has recently been shown how to extract this branching ratio from neutral kaon decay data. We point out that the impact of indirect CP violation on the standard-model prediction of this mode, while nominally of order |ϵK| ∼ 10−3, is enhanced by a large amplitude ratio and leads to a shift of the branching ratio Br(KS → μ+μ−)ℓ=0 by a few percent, depending on the size of a relative phase that can be extracted from data. We also update the standard-model prediction of the short-distance contribution.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
L.S. Littenberg, The CP Violating Dacay \( {K}_L^0\to {\pi}^0\nu \overline{\nu} \), Phys. Rev. D 39 (1989) 3322 [INSPIRE].
Y. Grossman and Y. Nir, \( {K}_L\to {\pi}^0\nu \overline{\nu} \) beyond the standard model, Phys. Lett. B 398 (1997) 163 [hep-ph/9701313] [INSPIRE].
F. Mescia and C. Smith, Improved estimates of rare K decay matrix-elements from Kl3 decays, Phys. Rev. D 76 (2007) 034017 [arXiv:0705.2025] [INSPIRE].
J. Brod, M. Gorbahn and E. Stamou, Two-Loop Electroweak Corrections for the \( K\to \pi \nu \overline{\nu} \) Decays, Phys. Rev. D 83 (2011) 034030 [arXiv:1009.0947] [INSPIRE].
KOTO collaboration, Study of the \( {K}_L\to {\pi}^0\nu \overline{\nu} \) Decay at the J-PARC KOTO Experiment, Phys. Rev. Lett. 126 (2021) 121801 [arXiv:2012.07571] [INSPIRE].
G. Isidori and R. Unterdorfer, On the short distance constraints from KL,S → μ+μ−, JHEP 01 (2004) 009 [hep-ph/0311084] [INSPIRE].
G. D’Ambrosio and T. Kitahara, Direct CP Violation in K → μ+μ−, Phys. Rev. Lett. 119 (2017) 201802 [arXiv:1707.06999] [INSPIRE].
A. Dery, M. Ghosh, Y. Grossman and S. Schacht, K → μ+μ− as a clean probe of short-distance physics, JHEP 07 (2021) 103 [arXiv:2104.06427] [INSPIRE].
Particle Data Group collaboration, Review of Particle Physics, PTEP 2022 (2022) 083C01 [INSPIRE].
C. Bobeth, M. Gorbahn and E. Stamou, Electroweak Corrections to Bs,d → ℓ+ℓ−, Phys. Rev. D 89 (2014) 034023 [arXiv:1311.1348] [INSPIRE].
T. Hermann, M. Misiak and M. Steinhauser, Three-loop QCD corrections to Bs → μ+μ−, JHEP 12 (2013) 097 [arXiv:1311.1347] [INSPIRE].
C. Bobeth et al., Bs,d → l+l− in the Standard Model with Reduced Theoretical Uncertainty, Phys. Rev. Lett. 112 (2014) 101801 [arXiv:1311.0903] [INSPIRE].
G. Buchalla and A.J. Buras, \( K\to \pi \nu \overline{\nu} \) and high precision determinations of the CKM matrix, Phys. Rev. D 54 (1996) 6782 [hep-ph/9607447] [INSPIRE].
V. Cirigliano et al., Kaon Decays in the Standard Model, Rev. Mod. Phys. 84 (2012) 399 [arXiv:1107.6001] [INSPIRE].
G. Buchalla, A.J. Buras and M.E. Lautenbacher, Weak decays beyond leading logarithms, Rev. Mod. Phys. 68 (1996) 1125 [hep-ph/9512380] [INSPIRE].
K. Anikeev et al., B physics at the Tevatron: Run II and beyond, (2001) [INSPIRE].
T. Huber, E. Lunghi, M. Misiak and D. Wyler, Electromagnetic logarithms in \( \overline{B}\to {X}_s{l}^{+}{l}^{-} \), Nucl. Phys. B 740 (2006) 105 [hep-ph/0512066] [INSPIRE].
M. Awramik, M. Czakon, A. Freitas and G. Weiglein, Precise prediction for the W boson mass in the standard model, Phys. Rev. D 69 (2004) 053006 [hep-ph/0311148] [INSPIRE].
Flavour Lattice Averaging Group (FLAG) collaboration, FLAG Review 2021, Eur. Phys. J. C 82 (2022) 869 [arXiv:2111.09849] [INSPIRE].
A. Dery et al., A Precision Relation between Γ(K → μ+μ−)(t) and \( \mathcal{B}\left({K}_L\to {\mu}^{+}{\mu}^{-}\right)/\mathcal{B}\left({K}_L\to \gamma \gamma \right) \), JHEP 03 (2023) 014 [arXiv:2211.03804] [INSPIRE].
A.J. Buras and E. Venturini, Searching for New Physics in Rare K and B Decays without |Vcb| and |Vub| Uncertainties, Acta Phys. Polon. B 53 (2021) A1 [arXiv:2109.11032] [INSPIRE].
Acknowledgments
We thank Andrzej Buras, Giancarlo D’Ambrosio, Avital Dery, Yuval Grossman, Christopher Smith, and Jure Zupan for discussions. JB thanks the Physics Department at the Weizmann Institute for Science for hospitality, and acknowledges support in part by DoE grant DE- SC0011784.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2209.07445
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Brod, J., Stamou, E. Impact of indirect CP violation on Br(KS → μ+μ−)ℓ=0. J. High Energ. Phys. 2023, 155 (2023). https://doi.org/10.1007/JHEP05(2023)155
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP05(2023)155