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