Indirect upper limits on $\ell_i\to\ell_j\gamma\gamma$ from $\ell_i\to\ell_j\gamma$

TL;DR

This paper uses effective field theory to establish indirect, model-independent upper limits on lepton flavor violating decays involving two photons, based on existing bounds on single-photon decays, significantly improving current constraints.

Contribution

It provides the first model-independent indirect upper limits on $ au o ext{ell}\gamma ext{gamma}$ decays derived from $ au o ext{ell}\gamma$ bounds, enhancing the sensitivity of rare decay searches.

Findings

Indirect limits are about 1000 times stronger than direct bounds for $ au o ext{ell}\gamma ext{gamma}$.

Current bounds on $ au o ext{ell}\gamma ext{gamma}$ are four orders of magnitude weaker than the indirect limits.

Highlights the importance of Belle II or Super Tau Charm Facility for discovering $ au o ext{ell}\gamma ext{gamma}$.

Abstract

We perform an effective field theory analysis to correlate the charged lepton flavor violating processes $\ell_i\to\ell_j\gamma\gamma$ and $\ell_i\to\ell_j\gamma$. Using the current upper bounds on the rate for $\ell_i\to\ell_j\gamma$, we derive model-independent upper limits on the rates for $\ell_i\to\ell_j\gamma\gamma$. Our indirect limits are about three orders of magnitude stronger than the direct bounds from current searches for $\mu\to e\gamma\gamma$, and four orders of magnitude better than current bounds for $\tau\to\ell\gamma\gamma$. We also stress the relevance of Belle II or a Super Tau Charm Facility to discover the rare decay $\tau\to\ell\gamma\gamma$.