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.