A leptoquark and vector-like quark extended model for the simultaneous explanation of the $W$ boson mass and muon $g-2$ anomalies
The CDF collaboration recently announced a new measurement result of the $W$ boson mass, and it is in tension with the standard model (SM) prediction. In this paper, we explain this anomaly in the vector-like quark (VLQ) $(X,T,B)_{L,R}$ and leptoquark (LQ) $S_3$ extended model. In this model, both the VLQ and LQ have positive corrections to the $W$ boson mass. Moreover, it can also be a solution to the $(g-2)_{\mu}$ anomaly because of the chiral enhancements from top, $T$, and $B$ quarks.