Exploration of the MSSM with Non-Universal Higgs Masses

TL;DR

This paper extends MSSM studies by allowing non-universal Higgs soft masses (NUHM), freeing $\mu$ and $m_A$ from CMSSM constraints and enabling a detailed confrontation with accelerator and dark-matter data. The authors derive low-energy spectra with NUHM boundary conditions, highlight the impact of the nonzero $S$-term on renormalization-group evolution, and systematically explore the NUHM parameter space across key planes: $(m_{1/2}, m_0)$, $(\mu, m_A)$, and $(\mu, M_2)$. They show that, unlike CMSSM, the NUHM can accommodate smaller $m_A$ (for large $\tan\beta$) while the LSP mass remains close to the CMSSM lower bound, and they identify rich coannihilation and funnel structures that shape the cosmologically acceptable regions. The study provides a comprehensive coannihilation framework (Appendices A–D) and demonstrates how updated collider and $g-2$ data interact with NUHM dynamics to constrain the viable MSSM landscape, pointing to further avenues such as nonzero $A_0$ exploration and broader scans over $\tan\beta$ and soft terms.

Abstract

We explore the parameter space of the minimal supersymmetric extension of the Standard Model (MSSM), allowing the soft supersymmetry-breaking masses of the Higgs multiplets, m_{1,2}, to be non-universal (NUHM). Compared with the constrained MSSM (CMSSM) in which m_{1,2} are required to be equal to the soft supersymmetry-breaking masses m_0 of the squark and slepton masses, the Higgs mixing parameter mu and the pseudoscalar Higgs mass m_A, which are calculated in the CMSSM, are free in the NUHM model. We incorporate accelerator and dark matter constraints in determining allowed regions of the (mu, m_A), (mu, M_2) and (m_{1/2}, m_0) planes for selected choices of the other NUHM parameters. In the examples studied, we find that the LSP mass cannot be reduced far below its limit in the CMSSM, whereas m_A may be as small as allowed by LEP for large tan β. We present in Appendices details of the calculations of neutralino-slepton, chargino-slepton and neutralino-sneutrino coannihilation needed in our exploration of the NUHM.

Figures (10)

• Figure 1: The CMSSM $(m_{1/2}, m_0)$ planes for (a) $\tan \beta = 10$ and $\mu > 0$, (b) $\tan \beta = 10$ and $\mu < 0$, (c) $\tan \beta = 35$ and $\mu < 0$ and (d) $\tan \beta = 50$ and $\mu > 0$, assuming $A_0 = 0, m_t = 175$ GeV and $m_b(m_b)^{\overline {MS}}_{SM} = 4.25$ GeV. The near-vertical (red) dot-dashed lines are the contours $m_h = 114$ GeV as calculated using FeynHiggsFeynHiggs, and the near-vertical (black) dashed line in panel (a) is the contour $m_{\chi^\pm} = 103.5$ GeV. The medium (dark green) shaded regions are excluded by $b \to s \gamma$, and the light (turquoise) shaded areas are the cosmologically preferred regions with $0.1\leq\Omega_{\chi} h^2\leq 0.3$. In the dark (brick red) shaded regions, the LSP is the charged ${\tilde{\tau}}_1$, so these regions are excluded. In panels (a) and (d), the regions allowed by the E821 measurement of $a_\mu$ at the 2-$\sigma$ level, as discussed in the text, are shaded (pink) and bounded by solid black lines, with dashed lines indicating the 1-$\sigma$ ranges.
• Figure 2: Projections of the NUHM model on the $(m_{1/2}, m_0)$ planes for $\tan \beta = 10$ and (a) $\mu = 400$ GeV and $m_{ A} = 400$ GeV, (b) $\mu = 400$ GeV and $m_{ A} = 700$ GeV, (c) $\mu = 700$ GeV and $m_{ A} = 400$ GeV and (d) $\mu = 700$ GeV and $m_{ A} = 700$ GeV, assuming $A_0 = 0, m_t = 175$ GeV and $m_b(m_b)^{\overline {MS}}_{SM} = 4.25$ GeV. The near-vertical (red) dot-dashed lines are the contours $m_h = 114$ GeV as calculated using FeynHiggsFeynHiggs, and the near-vertical (black) dashed lines are the contours $m_{\chi^\pm} = 103.5$ GeV. The dark (black) dot-dashed lines indicate the GUT stability constraint. There are two such lines for each panel and only the areas in between are allowed by this constraint. The light (turquoise) shaded areas are the cosmologically preferred regions with $0.1\leq\Omega_{\chi} h^2\leq 0.3$. The dark (brick red) shaded regions is excluded because a charged particle is lighter than the neutralino, and the darker (dark blue) shaded regions is excluded because the LSP is a sneutrino. In panel (c) there is a very small medium (green) shaded region excluded by $b \to s \gamma$, at small $m_{1/2}$. The regions allowed by the E821 measurement of $a_\mu$ at the 2-$\sigma$ level, as discussed in the text, are shaded (pink) and bounded by solid black lines.
• Figure 3: The NUHM $(m_{1/2}, m_0)$ planes for (a) $\tan \beta = 10$ , (b) $\tan \beta = 20$, (c) $\tan \beta = 35$ and (d) $\tan \beta = 50$, for $\mu = 400$ GeV, $m_{ A} = 700$ GeV, assuming $A_0 = 0, m_t = 175$ GeV and $m_b(m_b)^{\overline {MS}}_{SM} = 4.25$ GeV. The shadings and line styles are the same as in Fig. \ref{['fig:2']}.
• Figure 4: The NUHM $(\mu, m_{ A})$ planes for $\tan \beta = 10$, (a) $m_0 = 100$ GeV and $m_{1/2} = 300$ GeV, (b) $m_0 = 100$ GeV and $m_{1/2} = 500$ GeV, (c) $m_0 = 300$ GeV and $m_{1/2} = 300$ GeV and (d) $m_0 = 300$ GeV and $m_{1/2} = 500$ GeV, assuming $A_0 = 0, m_t = 175$ GeV and $m_b(m_b)^{\overline {MS}}_{SM} = 4.25$ GeV. The shadings and line styles are the same as in Fig. \ref{['fig:2']}.
• Figure 5: The masses $m_\chi$ (dark solid), $m_{\chi^\pm}$ (dark dashed), $m_{\widetilde{\tau}_1}$ (light solid), $m_{\widetilde{e}_R}$ (light dashed), $m_{\widetilde{\nu}_\tau}$ (thin solid) and $m_{\widetilde{\nu}_e}$ (thin dashed) as functions of $\mu$ for $\tan \beta = 10$, $m_{1/2} = 300$ GeV, $m_0 = 100$ GeV for (a) $m_{ A} = 200$ GeV and (b) $m_{ A} = 600$ GeV, assuming $A_0 = 0, m_t = 175$ GeV and $m_b(m_b)^{\overline {MS}}_{SM} = 4.25$ GeV.