# Lepton-flavor-violating semileptonic $\tau$ decay and $K\to\pi\nu\bar\nu$

## TL;DR

This paper investigates lepton-flavor violation in semileptonic tau decays caused by new physics, showing that rare kaon decays currently provide stronger constraints than direct tau decay searches, with future experiments poised to further test these effects.

## Contribution

It demonstrates that constraints from rare kaon decays can surpass direct tau decay limits for certain new physics operators, highlighting the importance of complementary probes.

## Key findings

- Current kaon decay data impose stronger bounds than tau decay searches.
- Leptonic charged-meson decays also constrain some new physics operators.
- Upcoming experiments will significantly test the parameter space of these new physics effects.

## Abstract

We consider lepton-flavor violation in strangeness changing ($|\Delta S|=1$) semileptonic $\tau$-lepton decays arising from new physics encoded in a standard model effective Lagrangian. Its invariance under the standard model gauge group entails the relevance of other processes which can serve as complementary probes of the new physics operators. We show in particular that for some of them the bounds implied by current data on the rare kaon decays involving a neutrino pair, $K\to \pi\nu\bar\nu$, are stronger than the existing limits from direct searches for lepton-flavor-violating semileptonic $\tau$ decays. We discuss additional processes affected by the same operators and find that certain leptonic charged-meson decays also provide stricter constraints on a few more of them. Upcoming results of ongoing experiments such as Belle II and NA62 will further test the new physics parameter space.