Probing the Stop Sector of the MSSM with the Higgs Boson at the LHC

TL;DR

The paper introduces a Higgs-based method to probe the MSSM stop sector by exploiting the lightest CP-even Higgs mass $m_h$ and the gluon-fusion production rate ratio $R_g = \Gamma_g^{\text{MSSM}}/\Gamma_g^{\text{SM}}$. In the MSSM, both observables primarily constrain the stop-sector parameters $m^2_{ ilde t_L}$, $m^2_{ ilde t_R}$, and the mixing term $X_t$, with $|r| = |(m^2_{ ilde t_L}-m^2_{ ilde t_R})/(m^2_{ ilde t_L}+m^2_{ ilde t_R})|$ typically small (\lesssim 0.4); two measurements effectively determine the overall stop mass scale $m_{ ilde t}$ and $X_t/m_{ ilde t}$, especially when stops are light and mixing is large, aligning with minimized electroweak fine-tuning. The authors show that large $m_h$ with a notably reduced $R_g$ can be difficult to reconcile within MSSM without entering extreme parameter regions or invoking sbottom-sector effects at large $\tan\beta$, motivating future precision in $R_g$ and complementary analyses to test MSSM naturalness. The study highlights experimental/theoretical uncertainties, noting $m_h$ can be measured precisely at the LHC while $R_g$ carries larger (~30%) uncertainties, and discusses potential use of $gg\to h \to \gamma\gamma$ as an alternative observable when $R_g$ is hard to constrain.

Abstract

We propose using the lightest CP-even Higgs boson in the minimal supersymmetric standard model (MSSM) to probe the stop sector. Unlike measuring stop masses in production/decay processes which requires knowledge of masses and mixing angles of other superparticles, the strategy depends little on supersymmetric parameters other than those in the stop sector in a large region of parameter space. We show that measurements of the Higgs mass and the production rate in the gluon fusion channel, the dominant channel at the LHC, allow for determination of two parameters in the stop mass-squared matrix, including the off-diagonal mixing term. This proposal is very effective when stops are light and their mixing is large, which coincides with the region where the electroweak symmetry breaking is minimally fine tuned. We also argue that a lightest CP-even Higgs mass in the upper range of allowed values and a production rate significantly smaller than in the standard model would be difficult to reconcile within the MSSM, except in extreme corners of the parameter space.

Figures (4)

• Figure 1: Gluon fusion production of the Higgs boson in the standard model.
• Figure 2: Plot of $R_g$ as a function of $r$ for $m_{\tilde{t}}^2 = 500$ GeV, $\tan \beta = 10$ (green/gray), $\tan \beta = 30$ (red/dark gray), $\tan \beta = 50$ (blue/black). The solid lines are for other SUSY masses fixed to 400 GeV. For comparison, the (green/gray) dashed lines are for other SUSY masses fixed to 800 GeV and $\tan \beta = 10$. The three clusters of lines correspond to $X_t/m_{\tilde{t}} = 0,-1,-2$ as indicated in the plot.
• Figure 3: Plot of the Higgs boson mass as a function of $r$ for $m_{\tilde{t}}^2 = 500$ GeV, $\tan \beta = 10$ (green/gray), $\tan \beta = 30$ (red/dark gray), $\tan \beta = 50$ (blue/black). The solid lines are for other SUSY masses fixed to 400 GeV. For comparison, the (green/gray) dashed lines are for other SUSY masses fixed to 800 GeV and $\tan \beta = 10$. The three clusters of lines correspond to $X_t/m_{\tilde{t}} = 0,-1,-2$ as indicated in the plot.
• Figure 4: Contours of constant Higgs mass $m_h$ (GeV) (blue/black) and the gluon fusion rate $R_g$ (green/gray) in $m_{\tilde{t}}$ -- $X_t/m_{\tilde{t}}$ plane. The plot on the right zooms in on the region of small $m_{\tilde{t}}$ and large mixing $X_t/m_{\tilde{t}}$. All other SUSY masses are fixed to 400 GeV, $\tan \beta = 10$ and $\mu = 200$ GeV.