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Large numbers of muons will be produced at facilities developed to probelepton flavor violating process $\mu\to e\gamma$. We show that by constructinga suitable asymmetry, radiative muon decay $\mu\to e \gamma\nu_\mu\bar{\nu}_e$can also be used to test the $WW\gamma$ vertex at such facilities. The processhas two missing neutrinos in the final state and on integrating their momenta,the partial differential decay rate shows no radiation-amplitude-zero. Weestablish, however, that an easily separable part of the normalizeddifferential decay rate, odd under the exchange of photon and electronenergies, does have a zero in the case of standard model (SM). This "new typeof zero" has hitherto not been studied in literature. A suitably constructedasymmetry using this fact, enables a sensitive probe for the $WW\gamma$ vertexbeyond the SM. With a simplistic analysis, we find that the $C$ and $P$conserving dimension four $WW\gamma$ vertex can be probed at ${\calO}(10^{-2})$ with satisfactory significance level.

Testing $WW\gamma$ vertex in radiative muon decay