# Testing $WW\gamma$ vertex in radiative muon decay

Karan, Anirban (The Institute of Mathematical Sciences, Taramani, Chennai 600113, India and Homi Bhabha National Institute, BARC Training School Complex, Anushaktinagar, Mumbai 400094, India) ; Sinha, Rahul (The Institute of Mathematical Sciences, Taramani, Chennai 600113, India and Homi Bhabha National Institute, BARC Training School Complex, Anushaktinagar, Mumbai 400094, India) ; Mandal, Rusa (IFIC, Universitat de València-CSIC, Apartat de Correus 22085, E-46071 València, Spain)

12 February 2019

Abstract: Large numbers of muons will be produced at facilities developed to probe the lepton-flavor-violating process $\mu \to e\gamma$. We show that by constructing a suitable asymmetry, radiative muon decay $\mu \to e\gamma {\nu }_{\mu }{\overline{\nu }}_{e}$ can also be used to test the $WW\gamma$ vertex at such facilities. The process has two missing neutrinos in the final state, and upon integrating their momenta the partial differential decay rate shows no radiation-amplitude zero. However, we establish that an easily separable part of the normalized differential decay rate that is odd under the exchange of photon and electron energies does have a zero in the case of the standard model (SM). This new type of zero has hitherto not been studied in the literature. A suitably constructed asymmetry using this fact enables a sensitive probe for the $WW\gamma$ vertex beyond the SM. With a simplistic analysis, we find that the $C$- and $P$-conserving dimension-four $WW\gamma$ vertex can be probed at $O\left({10}^{-2}\right)$ with a satisfactory significance level.

Published in: Physical Review D 99 (2019)