Correlating the CDF W-mass shift with the muon g − 2 and the b → sℓ+ℓ− transitions

Motivated by the latest CDF W-mass measurement as well as the muon $g-2$ anomaly and the discrepancies observed in $b\to s{\ell }^{+}{\ell }^{-}$ transitions, we propose an extension of the Standard Model (SM) with the $SU{\left(2\right)}_L$-singlet vector-like fermion partners that are featured by additional $U{\left(1\right)}^{\prime }$ gauge symmetry. The fermion partners have the same SM quantum numbers as of the right-handed SM fermions, and can therefore mix with the latter after the electroweak and the $U{\left(1\right)}^{\prime }$ symmetry breaking. As a result, desirable loop-level corrections to the ${(g-2)}_{\mu }$, the W-boson mass $m_W$ and the Wilson coefficient $C_9$ in $b\to s{\mu }^{+}{\mu }^{-}$ transitions can be obtained. The final allowed parameter space is also consistent with the constraints from the $Z\to {\mu }^{+}{\mu }^{-}$ decay, the neutrino trident production and the LHC direct searches for the vector-like quarks and leptons.