Relic density of neutralino dark matter in supergravity models

Abstract

We calculate the relic density $({\ensuremath{\Omega}}_{{\ensuremath{\chi}}_{1}^{0}}{h}^{2})$ of neutralino dark matter in supergravity models with radiative electroweak symmetry breaking, for values of the Higgs sector parameter $\mathrm{tan}\ensuremath{\beta}\ensuremath{\equiv}{v}_{2}{/v}_{1}$ between the two infrared fixed points of the top quark Yukawa coupling, $\mathrm{tan}\ensuremath{\beta}\ensuremath{\simeq}1.8$ and $\mathrm{tan}\ensuremath{\beta}\ensuremath{\simeq}56$. For $\mathrm{tan}\ensuremath{\beta}\ensuremath{\lesssim}10$, the $\mathrm{CP}$-odd Higgs pseudoscalar ${(A}^{0})$ and the heavier $\mathrm{CP}$-even Higgs scalar ${(H}^{0})$ are much heavier than the lightest neutralino $({\ensuremath{\chi}}_{1}^{0})$, and the annihilation cross section of ${\ensuremath{\chi}}_{1}^{0}$ pairs is significantly enhanced only in the vicinity of the lighter $\mathrm{CP}$-even Higgs boson ${(h}^{0})$ and the $Z$ boson poles. For $\mathrm{tan}\ensuremath{\beta}\ensuremath{\gtrsim}40$, ${m}_{A}$ and ${m}_{H}$ become comparable to ${2m}_{{\ensuremath{\chi}}_{1}^{0}}$, 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, $0.1\ensuremath{\lesssim}{\ensuremath{\Omega}}_{{\ensuremath{\chi}}_{1}^{0}}{h}^{2}\ensuremath{\lesssim}0.5$, 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.