Constraint on the Photino Mass from Cosmology

A lower bound for the photino mass $m_{\tilde{\gamma }}$ as a function of the spin-0 fermion superpartner mass $m_{\tilde{f}}$ 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 $\tilde{\gamma }\tilde{\gamma }\to f\overline{f}$ into light fermions, and leads to a rather unexpected form for the bound: for $25 \mathrm{GeV}\lesssim m_{\tilde{f}}\lesssim 45 \mathrm{GeV}$, ${\left(m_{\tilde{\gamma }}\right)}_{min}\simeq m_{\tau }=1.8\mathrm{}$ GeV; for $m_{\tilde{f}}>45\mathrm{}$ GeV, ${\left(m_{\tilde{\gamma }}\right)}_{min}$ increases approximately linearly with $m_{\tilde{f}}$ to a value of 20 GeV when $m_{\tilde{f}}=100\mathrm{}$ GeV.