Impact of indirect CP violation on Br$(K_S\to {\mu }^{+}{\mu }^{-}{)}_{\ell =0}$

Abstract

The decay $K_S\to ({\mu }^{+}{\mu }^{-}{)}_{\ell =0}$, 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 $|{\epsilon }_K|\sim 10^{-3}$, is enhanced by a large amplitude ratio and leads to a shift of the branching ratio Br$(K_S\to {\mu }^{+}{\mu }^{-}{)}_{\ell =0}$ 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.

arXiv comment10 pages, no figures. Improved discussion, conclusions unchanged, version accepted for publication in JHEP

References in corpus (13)

• Weak Decays Beyond Leading Logarithms
• FLAG Review 2021
• Kaon Decays in the Standard Model
• Precise Prediction for the W-Boson Mass in the Standard Model
• Two-Loop Electroweak Corrections for the K -> pi nu anti-nu Decays
• Electromagnetic Logarithms in B -> X_s l+ l-
• Improved estimates of rare K decay matrix-elements from Kl3 decays
• On the short-distance constraints from K_{L,S} -> mu^+ mu^-
• Electroweak Corrections to $B_{s,d}\to {\ell }^{+}{\ell }^{-}$
• Three-loop QCD corrections to B_s -> mu^+ mu^-
• Direct $CP$ Violation in $K\to {\mu }^{+}{\mu }^{-}$
• $K\to {\mu }^{+}{\mu }^{-}$ as a clean probe of short-distance physics
• A Precision Relation between $\Gamma (K\to {\mu }^{+}{\mu }^{-})(t)$ and $\mathcal{B}(K_L\to {\mu }^{+}{\mu }^{-})/\mathcal{B}(K_L\to \gamma \gamma )$

Cited by in corpus (5)

• Beyond the Standard Model prospects for kaon physics at future experiments
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• A Precision Relation between $\Gamma (K\to {\mu }^{+}{\mu }^{-})(t)$ and $\mathcal{B}(K_L\to {\mu }^{+}{\mu }^{-})/\mathcal{B}(K_L\to \gamma \gamma )$
• Workshop summary -- Kaons@CERN 2023
• CP violation in $K\to {\mu }^{+}{\mu }^{-}$ with and without time dependence through a tagged analysis