Likelihood Analysis of the CMSSM Parameter Space

TL;DR

This paper develops a global likelihood framework for the CMSSM with universal $m_0$ and $m_{1/2}$, integrating LEP Higgs data, precision electroweak fits, $b \to s \gamma$, and optionally $g_\mu - 2$, together with the WMAP-reported relic density band $\Omega_{CDM} h^2$ and uncertainties in $m_t$ and $m_b$. The analysis shows a general preference for $\mu > 0$, with the coannihilation region typically favored over the focus-point region, though neither is excluded; the widths and locations of viable strips are highly sensitive to theoretical uncertainties in $m_t$ and $m_b$ and to the treatment of $g_\mu - 2$. Including $g_\mu - 2$ can significantly reshape allowed regions, especially depending on whether the $e^+e^-$ SM prediction for $g_\mu - 2$ is adopted. The resulting iso-likelihood contours map the CMSSM parameter space and offer guidance for future collider and dark-matter searches by identifying where viable CMSSM parameter space resides.

Abstract

We present a likelihood analysis of the parameter space of the constrained minimal supersymmetric extension of the Standard Model (CMSSM), in which the input scalar masses m_0 and fermion masses m_{1/2} are each assumed to be universal. We include the full experimental likelihood function from the LEP Higgs search as well as the likelihood from a global precision electroweak fit. We also include the likelihoods for b to s gamma decay and (optionally) g_mu - 2. For each of these inputs, both the experimental and theoretical errors are treated. We include the systematic errors stemming from the uncertainties in m_t and m_b, which are important for delineating the allowed CMSSM parameter space as well as calculating the relic density of supersymmetric particles. We assume that these dominate the cold dark matter density, with a density in the range favoured by WMAP. We display the global likelihood function along cuts in the (m_{1/2}, m_0) planes for tan beta = 10 and both signs of mu, tan beta = 35, mu < 0 and tan beta = 50, mu > 0, which illustrate the relevance of g_mu - 2 and the uncertainty in m_t. We also display likelihood contours in the (m_{1/2}, m_0) planes for these values of tan beta. The likelihood function is generally larger for mu > 0 than for mu < 0, and smaller in the focus-point region than in the bulk and coannihilation regions, but none of these possibilities can yet be excluded.

Figures (14)

• Figure 1: The likelihood function along slices in $m_0$ through the CMSSM parameter space for $\tan \beta = 10, A_0 = 0, \mu> 0$ and $m_{1/2} = 300, 800$ GeV in the left and right panels, respectively. The solid red curves show the total likelihood function and the green dashed curve is the likelihood function with $\Delta m_t = \Delta m_b = 0$. Both analyses include the $g_\mu - 2$ likelihood calculated using $e^+ e^-$ data. The horizontal lines show the 68% confidence level of the likelihood function for each case.
• Figure 2: As in Fig. \ref{['fig:WMAP']} for $\tan \beta = 10, A_0 = 0, \mu< 0$ and $m_{1/2} = 800$ GeV. The $g_\mu-2$ constraint is included (excluded) in the left (right) panels. In the right panel the 68% CLs for both cases are incidentally closed to each other.
• Figure 3: As in Fig. \ref{['fig:WMAP']}, but for slices at fixed $m_{1/2}$ that include also the focus-point region at large $m_0$. The red (solid) curves are calculated using the current errors in $m_t$ and $m_b$, the green dashed curve with no error in $m_t$, the violet dotted lines with $\Delta m_t = 0.5$ GeV, and the blue dashed-dotted lines with $\Delta m_t = 1$ GeV. In the upper two figures, the $g_\mu-2$ constraint has not been applied.
• Figure 4: The value of $\Omega_\chi h^2$ (solid) and $\partial \Omega h^2/\partial m_t$ (dashed) as functions of $m_0$ for $\tan \beta = 10, A_0 = 0, \mu> 0$ and $m_{1/2} = 300$ GeV, corresponding to the slice shown in Fig. \ref{['fig:WMAPFP']}c.
• Figure 5: As in Fig. \ref{['fig:WMAPFP']}, but for $\mu < 0$ and $m_{1/2} = 300$ GeV, including (excluding) the $g_\mu - 2$ contribution to the global likelihood in the left (right) panel.