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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 $SU(2)_L$-singletvector-like fermion partners that are featured by additional $U(1)^\prime$gauge symmetry. The fermion partners have the same SM quantum numbers as of theright-handed SM fermions, and can therefore mix with the latter after theelectroweak and the $U(1)^\prime$ symmetry breaking. As a result, desirableloop-level corrections to the $(g-2)_\mu$, the $W$-boson mass $m_W$ and theWilson coefficient $C_9$ in $b \to s \mu^+ \mu^-$ transitions can be obtained.The final allowed parameter space is also consistent with the constraints fromthe $Z \to \mu^+ \mu^-$ decay, the neutrino trident production and the LHCdirect searches for the vector-like quarks and leptons.

Correlating the CDF $W$-mass shift with the muon $g-2$ and the $b \to s \ell^+ \ell^-$ transitions