New physics contributions to ${\bar{B}}_s\to {\pi }^0({\rho }^0){\eta }^{{(}^{\mathrm{\prime }})}$ decays

The decay modes ${\bar{B}}_s\to {\pi }^0({\rho }^0){\eta }^{{(}^{\mathrm{\prime }})}$ are dominated by electroweak penguins that are small in the standard model. In this work we investigate the contributions to these penguins from a model with an additional $U(1{)}^{\mathrm{\prime }}$ gauge symmetry and show there effects on the branching ratios of ${\bar{B}}_s\to {\pi }^0({\rho }^0){\eta }^{{(}^{\mathrm{\prime }})}$. In a scenario of the model, where $Z^{\mathrm{\prime }}$ couplings to the left-handed quarks vanish, we show that the maximum enhancement occurs in the branching ratio of $\bar B^0_s\to ,\pi^0,\eta’$whereitcanreach$6$ times the SM prediction. On the other hand, in a scenario of the model where $Z^{\mathrm{\prime }}$ couplings to both left-handed and right-handed quarks do not vanish, we find that $Z^{\mathrm{\prime }}$ contributions can enhance the branching ratio of $B_s^0\to {\rho }^0\eta$ up to one order of magnitude comparing to the SM prediction for several sets of the parameter space where both $\mathrm{\Delta }{M}_{B_s}$ and $S_{\psi \varphi }$ constraints are satisfied. This kind of enhancement occurs for a rather fine-tuned point where $\mathrm{\Delta }{M}_{B_s}$ constraint on $\mid S_{SM}(B_s)+S_{Z^{\mathrm{\prime }}}(B_s)\mid$ is fulfilled by overcompensating the SM via $S_{Z^{\mathrm{\prime }}}(B_s)\simeq -2S_{SM}(B_s)$.