Indirect upper limits on ${\ell }_i\to {\ell }_j\gamma \gamma$ from ${\ell }_i\to {\ell }_j\gamma$

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 $\tau \to \ell \gamma \gamma$.

Comments: 5 pages, 3 figures