A model with vectorlike fermions and $U(1)_X$ symmetry: CKM unitarity, $b \rightarrow s$ transitions, and prospect at Belle II

The updated analysis of the LHCb Collaboration on the lepton flavor violation suggests that the new physics should couple to muons and electrons with comparable magnitudes, resulting in the anomalies in both rare decay channels, $b \rightarrow s \mu^+ \mu^-$ and $b \rightarrow s e^+ e^-$. Meanwhile, the recent result of the Muon $g-2$ experiment with higher precision has increased the existing tension with the standard model prediction. In this paper, we consider an extension of the standard model with a new sector consisting of vectorlike fermions and two scalar charged under an extra $U(1)_X$ gauge symmetry. The exotic Yukawa interactions in the this model lead to the quark mixing responsible for the additional contributions to the flavor changing neutral currents in $B$-meson decays, and solve the muon $g-2$ discrepancy. We derive the analytic expression of the new physics contributions to the Wilson coefficient $C_7$ in the effective Hamiltonian, and point out that the CKM unitarity violation can be explained within this context. By calculating the branching ratio of the inclusive radiative $B$ decay, the impact of current experimental data of the $b \rightarrow s \gamma$ transition on the model and the future prospect at the Belle II experiment are investigated. Taking into account the current data on the muon anomalous magnetic moment, the CKM unitarity violation, the constraints on the flavor observables relevant to the $b \rightarrow s$ transitions, the LHC searches for vectorlike quarks, and the perturbation limits of the couplings, the viable parameter regions of the model are identified.