Signatures of a Flavor Changing $Z'$ Boson in $B_q \to \gamma Z'$

Rare $B$ meson decays offer an opportunity to probe a light hidden $Z'$ boson. In this work we explore a new channel $B_q \to \gamma Z'$ ($q = d, s$) followed by a cascade decay of $Z'$ 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 $Z'$. For the first time, we calculate ${\rm BR}(B_q \to \gamma Z')$ 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 $B_d \to {\rm invisible} + \gamma$ 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 $Z'$ 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.