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The updated analysis of the LHCb Collaboration on the lepton flavor violationsuggests that the new physics should couple to muons and electrons withcomparable magnitudes, resulting in the anomalies in both rare decay channels,$b \rightarrow s \mu^+ \mu^-$ and $b \rightarrow s e^+ e^-$. Meanwhile, therecent result of the Muon $g-2$ experiment with higher precision has increasedthe existing tension with the standard model prediction. In this paper, weconsider an extension of the standard model with a new sector consisting ofvectorlike fermions and two scalar charged under an extra $U(1)_X$ gaugesymmetry. The exotic Yukawa interactions in the this model lead to the quarkmixing responsible for the additional contributions to the flavor changingneutral currents in $B$-meson decays, and solve the muon $g-2$ discrepancy. Wederive the analytic expression of the new physics contributions to the Wilsoncoefficient $C_7$ in the effective Hamiltonian, and point out that the CKMunitarity violation can be explained within this context. By calculating thebranching ratio of the inclusive radiative $B$ decay, the impact of currentexperimental data of the $b \rightarrow s \gamma$ transition on the model andthe future prospect at the Belle II experiment are investigated. Taking intoaccount the current data on the muon anomalous magnetic moment, the CKMunitarity violation, the constraints on the flavor observables relevant to the$b \rightarrow s$ transitions, the LHC searches for vectorlike quarks, and theperturbation limits of the couplings, the viable parameter regions of the modelare identified.

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