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The CDF collaboration has released a new measurement of the $W$ boson massusing their complete data set with 8.8 fb$^{-1}$ in $p\bar{p}$ collisions. Thisresult deviates from the Standard Model prediction by around 7$\sigma$. Weexplain how the two Higgs doublet model (2HDM) with vector-like quarks isaffected by the recently discovered W boson mass. In our study, we include boththeoretical constraints such as perturbative unitarity and vacuum stability aswell as a number of experimental constraints. We also look into how theeffective mixing angle, measured by the SLD collaboration in addition to theCDF W-boson mass, is used to determine the $S$ and $T$ parameters. In thealignment limit, we investigate the case where the lighter CP-even neutralHiggs boson of the 2HDM is the one found at the LHC and demonstrate how theparameter space of the 2HDM type II in the presence of vector-like quarks isconstrained. It is found that in most cases, there is a cancellation betweenthe 2HDM and vector-like quarks contributions, which enlarges the parameterspace of both models.

The oblique parameters in the 2HDM with Vector-Like Quarks: Confronting $M_W$ CDF-II Anomaly