Probing <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>μ</mml:mi><mml:mi>e</mml:mi><mml:mi>γ</mml:mi><mml:mi>γ</mml:mi></mml:math> contact interactions with <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> conversion
Sacha Davidson, Y. Kuno, Yuichi Uesaka, Masato Yamanaka
Abstract
Contact interactions of a muon, an electron and two photons can contribute to the decay $\ensuremath{\mu}\ensuremath{\rightarrow}e\ensuremath{\gamma}\ensuremath{\gamma}$, but also to the conversion of a muon into an electron in the electric field of a nucleus. We calculate the $\ensuremath{\mu}\ensuremath{\rightarrow}e$ conversion rate, and show that for the coefficients of operators involving the combination $FF\ensuremath{\propto}|\stackrel{\ensuremath{\rightarrow}}{E}{|}^{2}$ (as opposed to $F\stackrel{\texttildelow{}}{F}\ensuremath{\propto}\stackrel{\ensuremath{\rightarrow}}{E}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{B}$), the current bound on $\ensuremath{\mu}\ensuremath{\rightarrow}e$ conversion is more sensitive than the bound on $\ensuremath{\mu}\ensuremath{\rightarrow}e\ensuremath{\gamma}\ensuremath{\gamma}$.