We present detailed calculations of the X̃t̃ 1 coannihilation channels that have the largest impact on the relic ̃X density in the constrained minimal supersymmetric extension of the Standard Model (CMSSM), in which scalar masses m 0 , gaugino masses m 1/2 and the trilinear soft supersymmetry-breaking parameters A 0 are each assumed to be universal at some input grand unification scale. The most important t̃ 1 t̃ 1 * and t̃ 1 t̃ 1 annihilation channels are also calculated, as well as t̃ 1 ̃el coannihilation channels. We illustrate the importance of these new coannihilation calculations when A 0 is relatively large. While they do not increase the range of m 1/2 and hence m χ allowed by cosmology, these coannihilation channels do open up new 'tails' of parameter space extending to larger values of m 0 .
Bibliographical noteFunding Information:
We thank Toby Falk for many related discussions. The work of K.A.O. and Y.S. was supported in part by DOE grant DE-FG02-94ER-40823. Appendix A We calculate the tree contributions to the coannihilation and annihilation amplitudes that are leading order in α s , α t ≡ λ t 2 /4π and/or α b ≡ λ b 2 /4π. We keep terms that are of the same order in α s α em , α t α em , α b α em , α s α W , α t α W and/or α b α W , but neglect most terms in α em and/or α W . This approximation is motivated by the relatively large magnitudes of α s and α t , and the fact that α b ∼ α t at large tan β . We have however included s-channel Z , and γ exchange for t ̃ 1 t ̃ 1 ∗ →t t ̄ and checked that they make negligible contribution to the total cross section and therefore neglect these channels in the remaining amplitudes. A.1