Calculations of Neutralino-Stop Coannihilation in the CMSSM

TL;DR

This paper addresses the neutralino relic density in the CMSSM by incorporating neutralino-stop coannihilation channels, especially when the trilinear parameter $A_0$ is large. It develops and applies the formalism for coannihilations, calculating leading ${\tilde{\chi}}{\tilde{t}}_1$, ${\tilde{t}}_1{\tilde{t}}_1^*$, ${\tilde{t}}_1{\tilde{t}}_1$, and ${\tilde{t}}_1{\tilde{\ell}}$ processes, and shows that specific channels such as ${\tilde{\chi}}{\tilde{t}}_1 \to t g$ and $t h$ can dominate the effective annihilation rate. The results reveal that, while these coannihilations do not extend the maximum $m_{1/2}$, they create a substantial high-$m_0$ tail in the CMSSM parameter space compatible with cosmology, with the tail’s extent sensitive to $A_0$ and to constraints like $b \to s\gamma$ and $g_\mu-2$. The Appendix provides detailed matrix elements enabling replication and broader MSSM application, underscoring the broader relevance of stop-related coannihilations in SUSY dark-matter phenomenology.

Abstract

We present detailed calculations of the neutralino-stop coannihilation channels that have the largest impact on the relic neutralino density in the constrained minimal supersymmetric extension of the Standard Model (CMSSM), in which scalar masses m_0, gaugino masses m_1/2 and the trilinear soft supersymmetry-breaking parameters A_0 are each assumed to be universal at some input grand unification scale. The most important stop-stop* and stop-stop annihilation channels are also calculated, as well as stop-slepton coannihilation channels. We illustrate the importance of these new coannihilation calculations when A_0 is relatively large. While they do not increase the range of m_1/2 and hence neutralino mass allowed by cosmology, these coannihilation channels do open up new `tails' of parameter space extending to larger values of m_0.

Figures (7)

• Figure 1: The separate contributions to the ${\widetilde{\chi}} {\tilde{t}_1}$ coannihilation cross sections $\hat{\sigma}\equiv a+{1\over2}b x$ for $x=T/m_{\widetilde{\chi}}=1/23$ as functions of $m_0$ for (a) $m_{1\!/2} = 230{\rm \, Ge V}$, $A_0 = 1000{\rm \, Ge V}$ and (b) $m_{1\!/2} = 450{\rm \, Ge V}$, $A_0 = 2000{\rm \, Ge V}$. Also shown are the total cross section and , for comparison, the much smaller total cross section for ${\widetilde{\chi}} {\widetilde{\chi}}$ annihilation.
• Figure 2: The separate contributions to the ${\tilde{t}_1} {\tilde{t}_1}^*$ annihilation cross sections $\hat{\sigma}\equiv a+{1\over2}b x$ for $x=T/m_{\widetilde{\chi}}=1/23$, as functions of $m_0$ for (a) $m_{1\!/2} = 230{\rm \, Ge V}$, $A_0 = 1000{\rm \, Ge V}$ and (b) $m_{1\!/2} = 450{\rm \, Ge V}$, $A_0 = 2000{\rm \, Ge V}$. Also shown are the total cross section and, for comparison, the much smaller total cross section for ${\widetilde{\chi}} {\widetilde{\chi}}$ annihilation.
• Figure 3: The ${\tilde{t}_1} {\tilde{t}_1} \to t t$ annihilation cross sections $\hat{\sigma}\equiv a+{1\over2}b x$ for $x=T/m_{\widetilde{\chi}}=1/23$, as functions of $m_0$ for (a) $m_{1\!/2} = 230{\rm \, Ge V}$, $A_0 = 1000{\rm \, Ge V}$ and (b) $m_{1\!/2} = 450{\rm \, Ge V}$, $A_0 = 2000{\rm \, Ge V}$. Also shown, for comparison, is the much smaller total cross section for ${\widetilde{\chi}} {\widetilde{\chi}}$ annihilation.
• Figure 4: The separate contributions to the ${\tilde{\ell}_1} {\tilde{t}_1}$ coannihilation cross sections $\hat{\sigma}\equiv a+{1\over2}b x$ for $x=T/m_{\widetilde{\chi}}=1/23$, as functions of $m_0$ for (a) $m_{1\!/2} = 230{\rm \, Ge V}$, $A_0 = 1000{\rm \, Ge V}$ and (b) $m_{1\!/2} = 450{\rm \, Ge V}$, $A_0 = 2000{\rm \, Ge V}$. Also shown, for comparison, is the much smaller total cross section for ${\widetilde{\chi}} {\widetilde{\chi}}$ annihilation.
• Figure 5: The separate contributions to the total effective cross sections $\hat{\sigma}_{\rm eff}$ for $x=T/m_{\widetilde{\chi}}=1/23$, as functions of $\Delta M\equiv(m_{\tilde{\tau}_R}- m_{\widetilde{\chi}})/m_{\widetilde{\chi}}$, obtained by varying $m_{1/2}$, with (a) $A_0 = 1000{\rm \, Ge V}$ and (b) $A_0 = 2000{\rm \, Ge V}$, both for $\tan \beta = 10, \mu > 0$ and $m_0 = 300{\rm \, Ge V}$.