The sensitivity of $μ\to e$ processes to $τ$ flavour change

Transforming a $μ$ to a $τ$, then the $τ$ to to an $e$, results in $μ\to e$. In an EFT framework, we explore the sensitivity of $μ\to e$ observables to products of $(μ\to τ)\times (τ\to e)$ interactions, and show that the exceptional sensitivity of upcoming $μ\to e$ experiments could allow to probe parameter space beyond the reach of upcoming $τ\to l$ searches in Higgs, $τ$ and $B$ decays. We describe the $τ\to l$ interactions as dimension six operators in the SM EFT, identify pairs of them giving interesting contributions to $μ\to e$ processes, and obtain the anomalous dimensions mixing those pairs into dimension eight $μ\to e$ operators. We find that $μ\to e$ processes are sensitive to $τ$ flavour-changing $B$ decays at rates comparable to current $B$ anomalies, but cannot reduce rates -- as appropriate in many current $B$ anomalies -- because they do not interfere with the SM.

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