Partial wave treatment of supersymmetric dark matter in the presence ofCPviolation

Abstract

We present an improved partial wave analysis of the dominant lightest supersymmetric particle (LSP) annihilation channel to a fermion-antifermion pair which avoids the nonrelativistic expansion being therefore applicable near thresholds and poles. The method we develop allows for contributions of any partial wave in the total angular momentum $J$ in contrast to partial wave analyses in terms of the orbital angular momentum $L$ of the initial state, which is usually truncated to $p$ waves, and yields very accurate results. The method is formulated in such a way as to allow easy handling of $CP$-violating phases residing in supersymmetric parameters. We apply this refined partial wave technique in order to calculate the neutralino relic density in the constrained minimal supersymmetric standard model (CMSSM) in the presence of $CP$-violating terms occurring in the Higgs-mixing parameter $\ensuremath{\mu}$ and trilinear $A$ coupling for large $\mathrm{tan}\ensuremath{\beta}$. The inclusion of $CP$-violating phases in $\ensuremath{\mu}$ and $A$ does not upset significantly the picture, and the annihilation of the LSPs to a $b\overline{b}$, through Higgs exchange, is still the dominant mechanism in obtaining cosmologically acceptable neutralino relic densities in regions far from the stau coannihilation and the ``focus point.'' Significant changes can occur if we allow for phases in the gaugino masses and, in particular, the gluino mass.