Impact of the CDF $W$-mass anomaly on two Higgs doublet model

We consider the implication of the recent CDF $W$-mass anomaly in the general framework of two Higgs doublet model. We find that the large deviation of the $S$ and $T$ parameters from their SM values of zero leads to the upper limit of about $1$ TeV on the heavy charged and neutral Higgs bosons when it is combined with the theoretical constraints from the perturbative unitarity and for the Higgs potential to be bounded from below.

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