The Lightest Higgs Boson Mass in Pure Gravity Mediation Model

TL;DR

This paper analyzes the lightest Higgs boson mass within the MSSM under pure gravity mediation, where scalar masses are set by the gravitino mass $m_{3/2}$ and gaugino masses arise from anomaly mediation. By requiring consistency with the observed dark matter density and, optionally, thermal leptogenesis, it derives an upper bound on the Higgs mass of about $132$ GeV, tightening to around $128$ GeV if leptogenesis is assumed, with the bound derived from the interplay between Higgs quartic coupling evolution, threshold effects, and the wino DM constraints. The work also explores the linkage between the Higgs mass and gaugino spectra, showing that higgsino threshold corrections can reduce the gluino mass relative to pure anomaly-mediated expectations, yielding potentially observable collider signatures. These predictions provide a concrete, testable framework connecting Higgs physics, DM relic abundance, and superpartner spectra in a minimal gravity-mediated SUSY breaking scenario.

Abstract

We discuss the lightest Higgs boson mass in the minimal supersymmetric Standard Model with "pure gravity mediation". By requiring that the model provides the observed dark matter density, we find that the lightest Higgs boson is predicted to be below 132GeV. We also find that the upper limit on the lightest Higgs boson mass becomes 128GeV, if we further assume thermal leptogenesis mechanism as the origin of baryon asymmetry of universe. The interrelations between the Higgs boson mass and the gaugino masses are also discussed.

Figures (6)

• Figure 1: Left) The lightest Higgs boson mass as a function of $M_{\rm SUSY}$ with $\mu_H = M_{\rm SUSY}$. The result is slightly lighter than the one in Ref. arXiv:1108.6077 due to the large $\mu$-term (see the right panel). Right) The lightest Higgs boson mass as a function of $\mu_H$ for $M_{\rm SUSY} = 100$ TeV. In both panels, the color bands show the $1\sigma$ error of the top quark mass, $m_{\rm top}= 173.2\pm0.9$ GeV arXiv:1107.5255, while we have taken the central value of the strong coupling constant, $\alpha(M_Z)=0.1184\pm 0.0007$arXiv:0908.1135. We have also fixed the gaugino masses to $M_1 = 900$ GeV, $M_2 = 300$ GeV and $M_3 =- 2500$ GeV as reference values, although the predicted Higgs boson mass is insensitive to the gaugino masses.
• Figure 2: The contour plot of the lightest Higgs boson mass. The bands for $m_h = 120,125,130,135,140$ GeV represent the effects of the theoretical uncertainty of the ratio $\mu_H/M_{\rm SUSY}$ to the lightest Higgs boson mass. We have assumed that $M_{\rm SUSY}/3<\mu_H<3M_{\rm SUSY}$. We have used the central values of the $1\sigma$ errors of the strong coupling constant and the top quark mass.
• Figure 3: The required reheating temperature of universe as a function of the wino mass for the consistent dark matter density. We have used the thermal relic density given in Refs. hep-ph/0610249arXiv:0706.4071. The color bands correspond to the $1\sigma$ error of the observed dark matter density, $\Omega h^2 = 0.1126\pm 0.0036$arXiv:1001.4538. For a detailed discussion see also Ref. Ibe:2004tg.
• Figure 4: Left) The lightest Higgs boson mass for a given wino mass. We also show the required reheating temperature for the successful wino dark matter scenario as dashed lines (see Fig. \ref{['fig:TR']}). Right) The lightest Higgs boson mass dependence on the theoretical uncertainty from the ratio $\tilde{m}_{3/2}/M_{\rm SUSY}$.
• Figure 5: The upper limit on the reheating temperature as a function of the lightest Higgs boson mass. The green band represents the effects of the theoretically uncertain ratio $\mu_H/M_{\rm SUSY}$ which we have taken between $M_{\rm SUSY}/3 < \mu_H < 3 M_{\rm SUSY}$. The effect of the theoretical uncertainty from the ratio $\tilde{m}_{3/2}/M_{\rm SUSY}$ can be read off from the right panel of Fig. \ref{['fig:Higgswino']}.