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

TL;DR

This study reevaluates the $W$-boson mass within the Lepton-Specific Two Higgs Doublet Model (LS-2HDM) in light of the CMS and CDF results. Through random scans generated with $\text{SARAH}$ and $\text{SPheno}$ and a comprehensive suite of theoretical and experimental constraints, it finds that the CMS $M_W$ value is readily accommodated, while the CDF central value can be approached only to about $2\sigma$ when oblique parameters $S,T,U$, the SM-like Higgs requirement, and LFU data are enforced. The analysis shows that the oblique parameters, together with LFU and the mass of the SM-like Higgs, play a crucial role in shaping the viable parameter space, typically favoring heavier Higgs masses and specific mass splittings (e.g., $m_{H^{\pm}}-m_A$ within tens of GeV). While the LS-2HDM can accommodate the CMS result robustly, it does not fully reconcile the CDF and CMS measurements within a single consistent parameter set, highlighting an enduring tension that guides future model-building and precision EW studies.

Abstract

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 $7σ$. 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 $|\cos(β-α)|\lesssim0.06$, $17\lesssim\tanβ\lesssim39$, $144\lesssim m_{h_2}\lesssim414$ GeV, and $435\lesssim m_{A,H^{\pm}}\lesssim685$ GeV, the model reproduces the 2024 CMS $W$-boson mass within $3σ$. 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 $\lesssim2σ$. 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 $2σ$ to the CDF results.

Figures (10)

• Figure 1: The relation between $\tan\beta$ and the mass of the LS-2HDM scalars, for $m_{h_2}$ (top-left), $m_A$ (top-right), $m_{H^\pm}$ (bottom-left) and $m_{h_1}$ (bottom-right). Color coding of solutions are described in detail in previous text and summarized as: Green points satisfy conditions G1 and G2, yellow points satisfy conditions G1, G2 and G3, blue points satisfy conditions G1, G2, G3 and G4, red points satisfy conditions G1, G2, G3 and G5. Solid black lines indicate ATLAS 13 TeV analysis observation limits and gray shaded areas are excluded by these analysis ATLAS:2020zmsATLAS:2021upq. In $\tan\beta$ vs $m_{h_1}$ plot (bottom-right), condition G3 is not applied. Dashed vertical lines represent the SM-like Higgs mass.
• Figure 2: The variation of the cross-sections $\sigma(gg \rightarrow h_2 \rightarrow \tau\tau)$ (top-left), $\sigma(gg \rightarrow h_2 \rightarrow WW)$ (top-right) and $\sigma(gg \rightarrow h_2 \rightarrow ZZ)$ (bottom) with respect to $m_{h_2}$. The color scheme is same as Fig. \ref{['fig:Hmasses_1']}, and black shaded areas are excluded by Refs. ATLAS:2020zmsATLAS:2017jagATLAS:2017otj
• Figure 3: The diagrams illustrating the contributions to LFU from the new Higgs bosons through decays of $Z-$boson.
• Figure 4: The variation of $\delta_{\mu\mu}$ with respect to $\tan\beta$ (left) and $\delta_{\tau\tau}$ with respect to $\tan\beta$ (right). Color coding of the plots is the same as Fig. \ref{['fig:Hmasses_1']}. The solid, dashed and dash dotted lines indicate deviations from the current limits by Eqn. \ref{['lu-zdecay']} within $1\sigma$, $2\sigma$, and $3\sigma$, respectively. For $\delta_{\mu\mu}$ (left), all solutions lie within 1$\sigma$ vicinity.
• Figure 5: The diagrams illustrating the contributions to LFU from the new Higgs bosons through decays of $\tau$.