Resolving the W-Boson Mass in the Lepton Specific Two Higgs Doublet Model

In 2022, the CDF Collaboration reported the $W$-boson mass, $M_W=80.4335\pm0.0094~\mathrm{GeV}$, which deviates from the Standard Model (SM) prediction, $M_W^{\rm SM}=80.357\pm0.006~\mathrm{GeV}$, by about $7\sigma$. By contrast, the CMS Collaboration obtained $M_W=80.3602\pm0.0099~\mathrm{GeV}$, very close to the SM global electroweak fit value of $\sim80.357~\mathrm{GeV}$. Motivated by this situation, we reassess the $W$-boson mass within the Lepton-Specific Two Higgs Doublet Model (LS-2HDM). 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. In the LS-2HDM, if $h_1$ is the SM-like Higgs at $m_{h_1}\simeq125$ GeV with $|\cos(\beta-\alpha)|\lesssim0.06$, $17\lesssim\tan\beta\lesssim39$, $144\lesssim m_{h_2}\lesssim414$ GeV, and $435\lesssim m_{A,H^{\pm}}\lesssim685$ GeV, the model reproduces the 2024 CMS $W$-boson mass within $3\sigma$. Solutions near the 2022 CDF value, $M_W=80.4335\pm0.0094~\mathrm{GeV}$, survive; however, after applying all constraints, including HiggsTools, they approach it at best within $\lesssim2\sigma$. Our findings emphasize that the LS-2HDM favors the CMS results consistently with the current experimental results. On the other hand, while one can accommodate also the CDF results in this model theoretically, up-to-date electroweak precision bounds on the oblique parameters $(S,T,U)$ together with the SM-like Higgs and LFU constraints exclude these solutions and our results for $W-$boson mass can be only as close as about $2\sigma$ to the CDF results.