## Abstract

We find that the phase appearing in the unitarity relation between B(K_{L}→ μ^{+}μ^{−}) and B(K_{L}→ γγ) is equal to the phase shift in the interference term of the time- dependent K → μ^{+}μ^{−} decay. A probe of this relation at future kaon facilities constitutes a Standard Model test with a theory precision of about 2%. The phase has further importance for sensitivity studies regarding the measurement of the time-dependent K → μ^{+}μ^{−} decay rate to extract the CKM matrix element combination ∣ V_{ts}V_{td}sin (β+ β_{s}) ∣ ≈ A^{2}λ^{5}η¯. We find a model-independent theoretically clean prediction, cos^{2}φ_{0} = 0.96 ± 0.03. The quoted error is a combination of the theoretical and experimental errors, and both of them are expected to shrink in the future. Using input from the large-N_{C} limit within chiral perturbation theory, we find a theory preference towards solutions with negative cos φ_{0}, reducing a four-fold ambiguity in the angle φ_{0} to a two-fold one.

Original language | English |
---|---|

Article number | 14 |

Journal | Journal of High Energy Physics |

Volume | 2023 |

Issue number | 3 |

DOIs | |

State | Published - Mar 2023 |

Externally published | Yes |

### Bibliographical note

Publisher Copyright:© 2023, The Author(s).

## Keywords

- CP Violation
- Kaons
- Rare Decays

## Fingerprint

Dive into the research topics of 'A precision relation between Γ(K → μ^{+}μ

^{−})(t) and B(KL→

^{μ+}

^{μ−})/B(KL→γγ)'. Together they form a unique fingerprint.