Constraint on the Photino Mass from Cosmology

Abstract

A lower bound for the photino mass ${m}_{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\gamma}}}$ as a function of the spin-0 fermion superpartner mass ${m}_{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{f}}$ is derived as an extension of the calculation of Lee and Weinberg. The Majorana nature of the photino induces a $p$-wave threshold for annihilation $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\gamma}}\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\gamma}}\ensuremath{\rightarrow}f\overline{f}$ into light fermions, and leads to a rather unexpected form for the bound: for $25 \mathrm{GeV}\ensuremath{\lesssim}{m}_{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{f}}\ensuremath{\lesssim}45 \mathrm{GeV}$, ${({m}_{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\gamma}}})}_{min}\ensuremath{\simeq}{m}_{\ensuremath{\tau}}=1.8$ GeV; for ${m}_{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{f}}>45$ GeV, ${({m}_{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\gamma}}})}_{min}$ increases approximately linearly with ${m}_{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{f}}$ to a value of 20 GeV when ${m}_{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{f}}=100$ GeV.