Relic Density of Neutralino Dark Matter in Supergravity Models

TL;DR

The paper addresses the relic density of neutralino dark matter within minimal supergravity (SUGRA) GUTs across the full range of $\tan\beta$ bounded by infrared fixed points. It employs helicity-amplitude calculations (HELAS) to evaluate all neutralino annihilation channels, coupled with relativistic Boltzmann averaging and a pole-transform to handle Breit-Wigner resonances, while RGEs produce the SUSY spectrum. It provides empirical formulas for $m_{χ^0_1}$ as a function of $m_{1/2}$ and $\sin\beta$, reveals resonant dips when $2m_{χ^0_1}$ aligns with $m_h$, $M_Z$, $m_A$, or $m_H$, and maps cosmologically interesting regions onto narrow bands in parameter space. The findings constrain the mSUGRA parameter space, notably in the $(m_{1/2},\tan\beta)$ plane, and illustrate how DM relic density data can pin down high-scale SUSY-breaking parameters and expected SUSY spectra. This work thus bridges particle physics and cosmology, providing practical guidance for future collider and cosmological investigations.

Abstract

We calculate the relic density ($Ω_{χ^0_1} h^2$) of neutralino dark matter in supergravity models with radiative electroweak symmetry breaking, for values of the Higgs sector parameter $\tanβ\equiv v_2/v_1$ between the two infrared fixed points of the top quark Yukawa coupling, $\tanβ\simeq 1.8$ and $\tanβ\simeq 56$. For $\tanβ\alt 10$, the CP-odd Higgs pseudoscalar ($A^0$) and the heavier CP-even Higgs scalar ($H^0$) are much heavier than the lightest neutralino ($χ^0_1$), and the annihilation cross section of $χ^0_1$ pairs is significantly enhanced only in the vicinity of the lighter CP-even Higgs boson ($h^0$) and the $Z$ boson poles. For $\tanβ\agt 40$, $m_A$ and $m_H$ become comparable to $2m_{χ^0_1}$, and the neutralino annihilation cross section can be significantly enhanced by the poles of the $H^0$ and the $A^0$ as well. For a cosmologically interesting relic density, $0.1 \alt Ω_{χ^0_1} h^2 \alt 0.5$, we find that the supergravity parameter space is tightly constrained. The mass spectra for supersymmetric particles are presented for unification mass parameters in the cosmologically interesting region.