Signatures of a Flavor Changing $Z^{\prime }$ Boson in $B_q\to \gamma Z^{\prime }$

Abstract

Rare $B$ meson decays offer an opportunity to probe a light hidden $Z^{\prime }$ boson. In this work we explore a new channel $B_q\to \gamma Z^{\prime }$ ($q=d,s$) followed by a cascade decay of $Z^{\prime }$ into an invisible (neutrino or dark matter) or charged lepton pair ${\ell }^{+}{\ell }^{-}$ ($\ell =e,\mu )$. The study is based on a simplified effective model where the down quark sector has tiny flavor-changing neutral current couplings with $Z^{\prime }$. For the first time, we calculate $\mathrm{BR}(B_q\to \gamma Z^{\prime })$ at the leading power of $1/m_b$ and $1/E_{\gamma }$. Confronting with the strong constraints from semi-invisible decays of $B$ meson, we find that the branching ratio for $B_d\to \mathrm{invisible}+\gamma$ can be larger than its Standard Model prediction, leaving a large room for new physics, in particular for light dark matter. Additionally, the branching ratio for $B_d\to e^{+}{e}^{-}\gamma$ can also be sizable when the corresponding flavor violating $Z^{\prime }$ coupling to quarks is of the axial-vector type. On the other hand, the predicted branching ratios of $B_d\to {\mu }^{+}{\mu }^{-}\gamma$ and $B_s\to {\ell }^{+}{\ell }^{-}\gamma$ are severely constrained by the experimental measurements.

Comments: 23 pages, 14 figures