Implications of a 125 GeV Higgs for the MSSM and Low-Scale SUSY Breaking

TL;DR

The paper investigates the implications of a SM-like Higgs with $m_h\approx125$ GeV for the MSSM and low-scale SUSY breaking. Using fixed $m_A$ and $\tan\beta$ benchmarks and the one-loop/leading two-loop structure of $m_h^2$, it shows that achieving $m_h\approx125$ GeV requires either heavy stops ($M_S$ in the TeV range) or sizable stop mixing with $|X_t|/M_S\approx\pm\sqrt{6}$, with a robust lower bound $\tan\beta\gtrsim3.5$ and weak dependence for $\tan\beta\gtrsim20$. The work then analyzes the consequences for gauge-mediated SUSY breaking, demonstrating that zero $A_t$ at the messenger scale generally forces a high messenger scale and/or heavy gauginos to generate the needed $|X_t|$ at the weak scale, often implying collider-stable NLSPs and potential high-scale tachyonic squarks. Overall, the results constrain mediation mechanisms and motivate MSSM extensions or non-minimal gauge mediation to accommodate a 125 GeV Higgs, with only modest expected deviations in Higgs production or decay rates.

Abstract

Recently, the ATLAS and CMS collaborations have announced exciting hints for a Standard Model-like Higgs boson at a mass of approximately 125 GeV. In this paper, we explore the potential consequences for the MSSM and low scale SUSY-breaking. As is well-known, a 125 GeV Higgs implies either extremely heavy stops (>~ 10 TeV), or near-maximal stop mixing. We review and quantify these statements, and investigate the implications for models of low-scale SUSY breaking such as gauge mediation where the A-terms are small at the messenger scale. For such models, we find that either a gaugino must be superheavy or the NLSP is long-lived. Furthermore, stops will be tachyonic at high scales. These are very strong restrictions on the mediation of supersymmetry breaking in the MSSM, and suggest that if the Higgs truly is at 125 GeV, viable models of gauge-mediated supersymmetry breaking are reduced to small corners of parameter space or must incorporate new Higgs-sector physics.

Figures (6)

• Figure 1: Contour plot of $m_{h}$ in the $\tan\beta$ vs. $X_t/M_S$ plane. The stops were set at $m_Q=m_U=2$ TeV, and the result is only weakly dependent on the stop mass up to $\sim 5$ TeV. The solid curve is $m_{h}=125$ GeV with $m_t=173.2$ GeV. The band around the curve corresponds to $m_{h}=$123-127 GeV. Finally, the dashed lines correspond to varying $m_t$ from 172-174.
• Figure 2: Contours of constant $m_{h}$ in the $M_{S}$ vs. $X_t$ plane, with $\tan\beta=30$ and $m_Q=m_U$. The solid/dashed lines and gray bands are as in fig. \ref{['fig:tanbeta']}.
• Figure 3: Contour plot of $X_t$ in the plane of physical stop masses $(m_{\tilde{t}_1},\, m_{\tilde{t}_2})$. Here $X_t$ is fixed to be the absolute minimum positive (left) or negative (right) solution to $m_h=125$ GeV.
• Figure 4: Values of running parameters: at left, in a case where $A_t$ is large and negative at low scales; at right, in a case where it is large and positive. The case $A_t < 0$ at low scales can be compatible with $A_t = 0$ from a high-scale mediation scheme, and in this case we expect that it is generally associated with tachyonic squarks at a high scale. Scalar masses are plotted as signed parameters, e.g. $m_Q^{(plotted)} \equiv m_Q^2/\left|m_Q\right|$.
• Figure 5: Messenger scale required to produce sufficiently large $|A_t|$ for $m_h=123$ GeV (left) and $m_h=125$ GeV (right) through renormalization group evolution.