Indirect upper limits on li -> lj gamma gamma from li -> lj gamma ℓi→ℓjγγ from ℓi→ℓjγ

We perform an effective field theory analysis to correlate the charged lepton flavor violating processes ℓi→ℓjγγ and ℓi→ℓjγ. Using the current upper bounds on the rate for ℓi→ℓjγ, we derive model-independent upper limits on the rates for ℓi→ℓjγγ. Our indirect limits are about three orders of magnitude stronger than the direct bounds from current searches for μ→eγγ, and four orders of magnitude better than current bounds for τ→ℓγγ. We also stress the relevance of Belle II or a Super Tau Charm Facility to discover the rare decay τ→ℓγγ.