Resolving the <i>W</i> boson mass in the lepton specific two Higgs doublet model*

Abstract In 2022, the collider detector at Fermilab (CDF) collaboration reported the W -boson mass ( ), which deviates from the standard model (SM) prediction ( ) by ~ . In contrast, the CMS collaboration obtained , which was very close to the SM global electroweak fit value of . Motivated by this situation, we reassess the W -boson mass within the lepton-specific two Higgs doublet model (LS-2HDM). To this end, we perform random scans (generated with SARAH 4.13.0 and evaluated with SPheno 4.0.3) and confront the results with up-to-date theoretical and experimental constraints. The scan enforces vacuum stability, perturbative unitarity, and perturbativity; electroweak precision observables via the oblique parameters ; LEP bounds on ; rare B -meson decays; lepton flavor universality (LFU) in Z and τ decays; and 13 TeV LHC searches for additional Higgs bosons. Viable points are further tested with HiggsTools (HiggsSignals + HiggsBounds). In the LS-2HDM, if is the SM-like Higgs at GeV with , , GeV, and GeV, the model reproduces the 2024 CMS W -boson mass within . Solutions near the 2022 CDF value ( ) survive; however, after applying all constraints, including HiggsTools, they approach it at best within . Our findings emphasize that LS-2HDM favors the CMS results consistently with the current experimental results. Although one can theoretically accommodate the CDF results in this model, up-to-date electroweak precision bounds on oblique parameters with the SM-like Higgs and LFU constraints exclude these solutions. Our results for -boson mass can only be as close as about to the CDF results .