The CMSSM Parameter Space at Large tan beta

Abstract

We extend previous combinations of LEP and cosmological relic density constraints on the parameter space of the constrained MSSM, with universal input supersymmetry-breaking parameters, to large tan beta. We take account of the possibility that the lightest Higgs boson might weigh about 115 GeV, but also retain the possibility that it might be heavier. We include the most recent implementation of the b to s gamma constraint at large tan beta. We refine previous relic density calculations at large tan beta by combining a careful treatment of the direct-channel Higgs poles in annihilation of pairs of neutralinos chi with a complete treatment of chi - stau coannihilation, and discuss carefully uncertainties associated with the mass of the b quark. We find that coannihilation and pole annihilations allow the CMSSM to yield an acceptable relic density at large tan beta, but it is consistent with all the constraints only if m_chi > 140 (180) GeV for mu > 0 (mu < 0) for our default choices m_b(m_b) = 4.25 GeV, m_t = 175 GeV, and A_0 = 0.

Figures (4)

• Figure 1: The $(m_{1/2}, m_0)$ planes for $\mu < 0$ and $\tan \beta =$ (a) 20, (b) 30, (c) 35 and (d) 37.5, found assuming $A_0 = 0, m_t = 175$ GeV and $m_b(m_b)^{\overline {MS}}_{SM} = 4.25$ GeV. In this case, we find no large allowed region for $\tan \beta \ge 40$. The near-vertical are the contours $m_{\chi^\pm} = 104$ GeV (dashed), $m_h = 113, 117$ GeV (dot-dashed). The medium (dark green) shaded regions are excluded by $b \to s \gamma$. The light (turquoise) shaded areas are the cosmologically preferred regions with $0.1\leq\Omega_{\chi} h^2\leq 0.3$. Away from the pole, above (below) these light-shaded areas, the relic density $\Omega_{\chi} h^2 > 0.3 (< 0.1)$. In the dark (brick red) shaded regions, the LSP is the charged ${\tilde{\tau}}_1$, so this region is excluded. The diagonal channel of low relic densities visible for $\tan \beta \ge 30$, flanked on both sides by cosmologically preferred regions, is due to direct-channel annihilation via the $A, H$ poles.
• Figure 2: The $(m_{1/2}, m_0)$ planes for $\mu > 0$ and $\tan \beta =$ (a) 30, (b) 40, (c) 50 and (d) 55, found assuming $A_0 = 0, m_t = 175$ GeV and $m_b(m_b)^{\overline {MS}}_{SM} = 4.25$ GeV. The near-vertical lines are the contours $m_{\chi^\pm} = 104$ GeV (dashed), $m_h = 113, 117$ GeV (dot-dashed). The medium (dark green) shaded regions are excluded by $b \to s \gamma$. 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 this region is excluded. The diagonal channel of low relic densities visible for $\tan \beta \ge 40$, flanked on both sides by cosmologically preferred regions, is due to direct-channel annihilation via the $A,H$ poles.
• Figure 3: Comparison between the $(m_{1/2}, m_0)$ planes for $m_b(m_b)^{\overline {MS}}_{SM} = 4.0$ and $4.5$ GeV. Panels (a, b) are for for $\mu < 0, \tan \beta = 35$ and panels (c, d) for $\mu > 0, \tan \beta = 50$. In all cases, we use $m_t = 175$ GeV and $A_0 = 0$. We see that the channel of low relic density due to rapid annihilation via the $A,H$ poles appears at smaller values of $m_{1/2} / m_0$ when $m_b(m_b)^{\overline {MS}}_{SM}$ is larger.
• Figure 4: Lower limits on the LSP mass $m_\chi$ obtained as functions of $\tan \beta$ for both signs of $\mu$. We use as defaults $m_b(m_b)^{\overline {MS}}_{SM} = 4.25$, $m_t = 175$ GeV and $A_0 = 0$.