Sensitivity of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>μ</mml:mi><mml:mo stretchy="false">→</mml:mo><mml:mi>e</mml:mi></mml:math> processes to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>τ</mml:mi></mml:math> flavor change
Marco Ardu, Sacha Davidson, Martin Gorbahn
Abstract
Transforming a $\ensuremath{\mu}$ to a $\ensuremath{\tau}$, then the $\ensuremath{\tau}$ to to an $e$, results in $\ensuremath{\mu}\ensuremath{\rightarrow}e$. In an effective field theory (EFT) framework, we explore the sensitivity of $\ensuremath{\mu}\ensuremath{\rightarrow}e$ observables to products of $(\ensuremath{\mu}\ensuremath{\rightarrow}\ensuremath{\tau})\ifmmode\times\else\texttimes\fi{}(\ensuremath{\tau}\ensuremath{\rightarrow}e)$ interactions and show that the exceptional sensitivity of upcoming $\ensuremath{\mu}\ensuremath{\leftrightarrow}e$ experiments could allow us to probe parameter space beyond the reach of upcoming $\ensuremath{\tau}\ensuremath{\leftrightarrow}l$ searches in Higgs, $\ensuremath{\tau}$, and $B$ decays. We describe the $\ensuremath{\tau}\ensuremath{\leftrightarrow}l$ interactions as dimension six operators in the SM EFT, identify pairs of them giving interesting contributions to $\ensuremath{\mu}\ensuremath{\leftrightarrow}e$ processes, and obtain the anomalous dimensions mixing those pairs into dimension eight $\ensuremath{\mu}\ensuremath{\rightarrow}e$ operators. We find that $\ensuremath{\mu}\ensuremath{\rightarrow}e$ processes are sensitive to $\ensuremath{\tau}$ flavor-changing $B$ decays at rates comparable to current $B$ anomalies, but lepton flavour violating operators cannot reduce B rates---as appropriate in many current $B$ anomalies---because they do not interfere with the SM.