Violation of lepton flavor and lepton flavor universality in rare kaon decays

Andreas Crivellin,Martin Hoferichter,Giancarlo D’Ambrosio,Lewis C Tunstall

doi:10.1103/physrevd.93.074038

Abstract

Recent anomalies in the decays of $B$ mesons and the Higgs boson provide hints towards lepton flavor (universality) violating physics beyond the Standard Model. We observe that four-fermion operators which can explain the $B$-physics anomalies have corresponding analogs in the kaon sector, and we analyze their impact on $K\to\pi\ell \ell'$ and $K\to\ell \ell'$ decays $(\ell=\mu,e)$. For these processes, we note the corresponding physics opportunities at the NA62 experiment. In particular, assuming minimal flavor violation, we comment on the required improvements in sensitivity necessary to test the $B$-physics anomalies in the kaon sector.

Highlights

The discovery of a Higgs-like resonance at the LHC experiments [1,2] provides the final ingredient to complete the Standard Model (SM) of particle physics
There are a variety of theoretical and phenomenological reasons to suspect that the SM is not the final theory, and that some form of new physics (NP) may be present near the electroweak scale
While no direct evidence for physics beyond the SM was found during the first LHC run, there are some interesting indirect hints for NP in the flavor sector, in the semileptonic decays of B mesons and the SM-forbidden decay h → μτ of the Higgs boson

Summary

PUZZLES IN THE FLAVOR SECTOR

The discovery of a Higgs-like resonance at the LHC experiments [1,2] provides the final ingredient to complete the Standard Model (SM) of particle physics. In the Higgs sector, CMS has presented results of a search for the lepton-flavor-violating (LFV) decay mode h → μτ, with a preferred value [21]. For the purely leptonic modes, the PDG average for Br1⁄2KL → μþμ− 1⁄4 ð6.84 Æ 0.11Þ × 10−6 is dominated by the E871 measurement [86], and the same experiment reported the sole observation of the electron mode, with branching fraction Br1⁄2KL → eþe− 1⁄4 9þ−46 × 10−12 [87] For later use, these results are conveniently expressed in terms of the ratios. The general picture that arises is the presence of long-distance physics, parametrized in terms of low-energy constants (LECs) in the effective weak Lagrangian The values of these LECs are poorly known in most cases, and this limits the predictive power of χPT3 in the weak sector.

FORMALISM

LEPTON-FLAVOR-VIOLATING DECAYS

CONCLUSIONS