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

Abstract

In 2022, the CDF Collaboration reported the $W$-boson mass, $M_W=80.4335\pm 0.0094\mathrm{GeV}$, which deviates from the Standard Model (SM) prediction, $M_W^{\mathrm{SM}}=80.357\pm 0.006\mathrm{GeV}$, by about $7\ddot{I}ƒ$. By contrast, the CMS Collaboration obtained $M_W=80.3602\pm 0.0099\mathrm{GeV}$, very close to the SM global electroweak fit value of $\sim 80.357\mathrm{GeV}$. 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 $m_{h_1}\simeq 125$ GeV with $|\cos ({\hat{I}}^2-\hat{I}\pm )|\lesssim 0.06$, $17\lesssim \tan {\hat{I}}^2\lesssim 39$, $144\lesssim m_{h_2}\lesssim 414$ GeV, and $435\lesssim m_{A,H^{\pm }}\lesssim 685$ GeV, the model reproduces the 2024 CMS $W$-boson mass within $3\ddot{I}ƒ$. Solutions near the 2022 CDF value, $M_W=80.4335\pm 0.0094\mathrm{GeV}$, survive; however, after applying all constraints, including HiggsTools, they approach it at best within $\lesssim 2\ddot{I}ƒ$. 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 $2\ddot{I}ƒ$ to the CDF results.