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Recently CDF II Collaboration reported that they measured W boson massprecisely. The measurement is deviated from the Standard Model (SM) Predictionat 7$\sigma$. Also, the recent FNAL measurement of the muon magnetic momentshows a $4.2\sigma$ deviation. To resolve the W boson as well as the muon$(g-2)$ anomalies, we explore the type-X two Higgs doublet model (2HDM). Weanalyze the $(m_A, \tan\beta)$ parameter space of the type-X 2HDM consistentwith the muon $(g-2)$, lepton universality test and recent $W$ boson massmeasurments from the CDF II collaboration. We find that the measurement of the$h\to AA$ branching ratio gives a strong lower mass bound on $m_H$.

Compatibility of muon $g-2$, $W$ mass anomaly in type-X 2HDM