Neutralino relic density in a Universe with a non-vanishing cosmological constant

TL;DR

This paper investigates the neutralino relic density within the CMSSM under the context of a flat, accelerating Universe with a nonzero cosmological constant. It combines a two-loop RGE-based SUSY spectrum calculation, analytic expressions for thermally averaged cross sections, and a robust numerical solution to the Boltzmann equation to predict ${\Omega}_{\tilde{\chi}} h^2$, explicitly including coannihilation with ${\tilde{\tau}}_R$ and resonance effects near poles and thresholds. The results show that cosmological and EW data constrain the CMSSM to narrow regions: a coannihilation-free band with ${M_{1/2} \lesssim 340\,\text{GeV}}$ and ${m_0 \lesssim 200\,\text{GeV}}$, or, at large ${\tan\beta}$ or near mass degeneracy with ${\tilde{\tau}_R}$, where coannihilation or ${A}$-pole processes can bring ${\Omega}_{\tilde{\chi}} h^2$ into the allowed range. A tighter CDM bound further favors the coannihilation scenario, with the actual relic density related to the no-coannihilation result by a reduction factor ${R(\Delta M)}$ depending on the mass splitting ${\Delta M}$. Overall, the work provides a concrete link between cosmological DM constraints and CMSSM parameter space, guiding expectations for SUSY searches at colliders.

Abstract

We discuss the relic density of the lightest of the supersymmetric particles in view of new cosmological data, which favour the concept of an accelerating Universe with a non-vanishing cosmological constant. Recent astrophysical observations provide us with very precise values of the relevant cosmological parameters. Certain of these parameters have direct implications on particle physics, e.g., the value of matter density, which in conjunction with electroweak precision data put severe constraints on the supersymmetry breaking scale. In the context of the Constrained Minimal Supersymmetric Standard Model (CMSSM) such limits read as: $M_{1/2} \simeq 300 \GeV - 340 \GeV$, $m_0 \simeq 80 \GeV - 130 \GeV$. Within the context of the CMSSM a way to avoid these constraints is either to go to the large $\tan β$ and $μ> 0$ region, or make ${\tilde τ}_R$, the next to lightest supersymmetric particle (LSP), be almost degenerate in mass with LSP.

Figures (11)

• Figure 1: The LSP relic density $\Omega_{\tilde{\chi}}\,h_0^2$ in the ($m_0$,$M_{1/2}$) plane for given values of $A_0$, $\tan \beta$ and sign of $\mu$. Grey tone regions, from darker to lighter, designate areas in which the LSP relic density takes values in the intervals: $0.00 -0.08$, $0.08-0.22$, $0.22-0.35$, $0.35-0.60$ and $0.60-1.00$ respectively. In the blanc area $\Omega_{\tilde{\chi}}\,h_0^2 > 1.0$. The area marked by " TH" is theoretically excluded (see main text). The area labelled by $m_{\tilde{C}}<95\; \mathrm{GeV}$ is excluded by chargino searches. Crosses denote points for which thresholds or poles are encountered.
• Figure 2: The relic density as function of $m_0$ for fixed values of the remaining parameters. The solid, dashed and dot-dashed lines correspond to $M_{1/2}=170$, $200$ and $400\; \mathrm{GeV}$ respectively.
• Figure 3: The relic density as function of $A_0$. The lines are as in figure \ref{['fig2']}.
• Figure 4: The relic density as function of $\tan \beta$. The lines are as in figure \ref{['fig2']}.
• Figure 5: The relic density as function of $M_{1/2}$. Crosses denote points that are near thresholds or poles. The solid (dashed) line corresponds to $m_0=150 \; (200) \; \mathrm{GeV}$.