The MSSM Parameter Space with Non-Universal Higgs Masses

TL;DR

This paper investigates the MSSM with non-universal Higgs masses (NUHM) by treating μ and m_A as independent EW-scale parameters and scanning the NUHM parameter space under cosmological relic-density bounds and collider/flavor constraints. By enforcing a neutral LSP and positivity of Higgs-mass-squared terms at the GUT scale, the study reveals richer and more diverse phenomenology than in the CMSSM, including bulk, coannihilation, and A/H-funnel regions across several two-dimensional planes such as (μ, m_A), (μ, M_2), (m_{1/2}, m_0), and (m_A, tanβ). Key findings show that μ > 0 is generally favored, m_A cannot be too small, and that coannihilation channels and direct-channel Higgs annihilation can dominate the relic density in different corners of parameter space; the GUT-scale positivity constraint remains a powerful filter. The work highlights the need for NUHM-aware benchmark scenarios and further exploration to fully understand the expanded MSSM landscape and its experimental implications.

Abstract

Without assuming that Higgs masses have the same values as other scalar masses at the input GUT scale, we combine constraints on the minimal supersymmetric extension of the Standard Model (MSSM) coming from the cold dark matter density with the limits from direct searches at accelerators such as LEP, indirect measurements such as b to s gamma decay and the anomalous magnetic moment of the muon. The requirement that Higgs masses-squared be positive at the GUT scale imposes important restrictions on the MSSM parameter space, as does the requirement that the LSP be neutral. We analyze the interplay of these constraints in the (mu, m_A), (mu, m_{1/2}), (m_{1/2}, m_0) and (m_A, tan beta) planes. These exhibit new features not seen in the corresponding planes in the constrained MSSM in which universality is extended to Higgs masses.

Figures (5)

• Figure 1: Compilations of phenomenological constraints on the MSSM with NUHM in the $(\mu, m_A)$ plane for $\tan \beta = 10$ and (a) $m_0 = 100$ GeV, $m_{1/2} = 300$ GeV, (b) $m_0 = 300$ GeV, $m_{1/2} = 1000$ GeV, assuming $A_0 = 0$, $m_t = 175$ GeV and $m_b(m_b)^{\overline {MS}}_{SM} = 4.25$ GeV. The light (turquoise) shading denotes the region where $0.1 < \Omega_\chi h^2 < 0.3$, and the (blue) solid line is the contour $m_\chi = m_A/2$, near which rapid direct-channel annihilation suppresses the relic density. The darker (green) shading shows the impact of the $b \to s \gamma$ constraint, and the darkest (red) shading shows where the LSP is charged. The dark (black) dashed line is the chargino constraint $m_{\chi^\pm} > 104$ GeV: lower $|\mu|$ values are not allowed. The lighter (red) dot-dashed line is the contour $m_h = 114$ GeV calculated using FeynHiggsFeynHiggs: lower $m_A$ values are not allowed. The dark (black) dot-dashed line indicates when one or another Higgs mass-squared becomes negative at the GUT scale: only lower $|\mu|$ and larger $m_A$ values are allowed. The crosses denote the values of $\mu$ and $m_A$ found in the CMSSM.
• Figure 2: Contours of the scaled Higgs masses ${\hat{m}_1}$ and ${\hat{m}_2}$ in the $(\mu, m_A)$ plane for $\tan \beta = 10$ and (a) $m_0 = 100$ GeV, $m_{1/2} = 300$ GeV, (b) $m_0 = 300$ GeV, $m_{1/2} = 1000$ GeV, assuming $A_0 = 0$, $m_t = 175$ GeV and $m_b(m_b)^{\overline {MS}}_{SM} = 4.25$ GeV. As in Fig. \ref{['fig:mumA10']}, the light (turquoise) shading denotes the region where $0.1 < \Omega_\chi h^2 < 0.3$. The darker shading denotes the region not excluded by the other constraints. The dark (black) lines correspond to contours of ${\hat{m}_2}$, and the lighter (red) lines to contours of ${\hat{m}_1}$. In (a) the thick solid contours correspond to ${\hat{m}} = 0$, the thick dashed contours to ${\hat{m}} = \pm 5$, and the thin solid contours to ${\hat{m}} = -15$. In (b) the thick solid contours correspond to ${\hat{m}} = 0$, the thick dashed contours to ${\hat{m}} = 2$, the thin solid contours to ${\hat{m}} = 3$, and the thin dashed contours to ${\hat{m}} = \pm 5$. The dark (blue) dashed lines at very low values of $m_A$ indicate the contours $\sin^2 (\beta - \alpha) = 0.7, 0.5$ and $0.3$, which decrease with $m_A$.
• Figure 3: Compilations of phenomenological constraints on the MSSM with NUHM in the $(\mu, M_2)$ plane for $\tan \beta = 10$ and (a) $m_0 = 100$ GeV, $m_A = 700$ GeV, (b) $m_0 = 400$ GeV, $m_A = 700$ GeV, again assuming $A_0 = 0$, $m_t = 175$ GeV and $m_b(m_b)^{\overline {MS}}_{SM} = 4.25$ GeV. The pale (turquoise) shading denotes the region where $0.1 < \Omega_\chi h^2 < 0.3$, and the (blue) solid line is the contour $m_\chi = m_A/2$, near which rapid direct-channel annihilation suppresses the relic density. The darker (green) shading shows the impact of the $b \to s \gamma$ constraint, and the darkest (red) shading shows where the LSP is charged. The dark (black) dashed line is the chargino constraint $m_{\chi^\pm} > 104$ GeV: lower values of $|\mu|$ and/or $M_2$ are not allowed. The lighter (red) dot-dashed line is the contour $m_h = 114$ GeV calculated using FeynHiggsFeynHiggs: lower $m_A$ are not allowed. The pale (pink) solid line shows the region excluded by $g_\mu - 2$. The dark (black) dot-dashed triangular line indicates when one or another Higgs mass-squared becomes negative at the GUT scale: only lower $|\mu|$ and intermediate $m_{1/2}$ are allowed. The (black) crosses denote the CMSSM points.
• Figure 4: Compilations of phenomenological constraints on the MSSM with NUHM in the $(m_{1/2}, m_0)$ plane for $\tan \beta = 10$ and (a) $\mu = 600$ GeV, $m_A = 400$ GeV, (b) $\mu = 400$ GeV, $m_A = 1000$ GeV, again assuming $A_0 = 0$, $m_t = 175$ GeV and $m_b(m_b)^{\overline {MS}}_{SM} = 4.25$ GeV. The pale (turquoise) shading denotes the region where $0.1 < \Omega_\chi h^2 < 0.3$, and the (blue) solid line is the contour $m_\chi = m_A/2$, near which rapid direct-channel annihilation suppresses the relic density. The darkest (red) shading shows where the LSP is charged. The dark (black) dashed line is the chargino constraint $m_{\chi^\pm} > 104$ GeV: lower $m_{1/2}$ are not allowed. The lighter (red) dot-dashed line is the contour $m_h = 114$ GeV calculated using FeynHiggsFeynHiggs: lower $m_{1/2}$ are not allowed. The light (pink) solid line is where the supersymmetric contribution to the muon anomalous moment is $a_\mu = 58 \times 10^{-10}$: lower $m_0$ and $m_{1/2}$ are excluded at the $2-\sigma$ level. The dark (black) dot-dashed lines indicates when one or another Higgs mass-squared becomes negative at the GUT scale: only intermediate values of $m_{1/2}$ are allowed in panel (a), and larger values in (b). The (black) cross in panel (b) denotes the CMSSM point.
• Figure 5: Compilations of phenomenological constraints on the MSSM with NUHM in the $(m_A, \tan \beta)$ plane for $(m_{1/2}, m_0, \mu) = {\rm (a)} (600, 800, 1000), {\rm (b)} (250, 1000, 200)$ GeV. The lighter (red) dot-dashed lines are the contours $m_h = 114$ GeV, the solid (blue) lines show where $m_\chi \sim m_A / 2$ and the dark (black) dot-dashed line indicates when one or another Higgs mass-squared becomes negative at the GUT scale. The light (turquoise) shading indicates where $0.1 < \Omega_\chi h^2 < 0.3$, the darker (green) shaded regions are excluded by the $b \to s \gamma$ constraint.