FCNC decays of standard model fermions into a dark photon

Abstract

We analyze a new class of FCNC processes, the $f \to f^{\prime} \, \bar{\gamma}$ decays of a fermion $f$ into a lighter (same-charge) fermion $f^{\prime}$ plus a {\it massless} neutral vector boson, a {\it dark photon} $\bar{\gamma}$. A massless dark photon does not interact at tree level with observable fields, and the $f \!\to\! f^{\prime} \, \bar{\gamma}$ decay presents a characteristic signature where the final fermion $f^{\prime}$ is balanced by a {\it massless invisible} system. Models recently proposed to explain the exponential spread in the standard-model Yukawa couplings can indeed foresee an extra unbroken {\it dark} $U(1)$ gauge group, and the possibility to couple on-shell dark photons to standard-model fermions via one-loop magnetic-dipole kind of FCNC interactions. The latter are suppressed by the characteristic scale related to the mass of heavy messengers, connecting the standard model particles to the dark sector. We compute the corresponding decay rates for the top, bottom, and charm decays ($t\to c\, \bar{\gamma},u\, \bar{\gamma}$, $\;b\to s\, \bar{\gamma},d\, \bar{\gamma}$, and $c\to u \bar{\gamma}$), and for the charged-lepton decays ($\tau \to \mu\, \bar{\gamma}, e\, \bar{\gamma}$, and $\mu \to e \bar{\gamma}$) in terms of model parameters. We find that large branching ratios for both quark and lepton decays are allowed in case the messenger masses are in the discovery range of the LHC. Implications of these new decay channels at present and future collider experiments are briefly discussed.