GeV scale dark matter and $B\rightarrow K+$ missing energy phenomenology in the $U(1)_{B-L}$ model

We elucidate the recently observed discrepancy in the branching ratio of $B^{+}\rightarrow K^{+}$ +inv decay mode using a GeV scale scalar dark matter in an anomaly-free $U(1)_{B-L}$ gauge extension of the Standard Model. We constrain the new parameters by using consistency with the existing bounds on Dark matter relic density, direct detection, collider and BR($B\rightarrow K^*\nu\bar{\nu}$) measured at the Belle II experiment. We investigate couplings between the mediator and the SM fermions as well as the dark matter particle. We then estimate the branching ratios of $b \to s \nu \bar \nu$ decay processes such as $B\rightarrow (K^+,K^*)\nu\bar{\nu}$, $B_s\rightarrow (\eta,\eta')\nu\bar{\nu}$, $ B_s\rightarrow \phi\nu\bar{\nu}$ and $B_c\rightarrow (D_s, D_s^*)\nu\bar{\nu}$ in a common parameter space, meeting the current experimental bounds of both sectors simultaneously.