Neutralino annihilation beyond leading order

Abstract

High-precision measurements of the relic dark matter density and the calculation of dark matter annihilation branching fractions in the sun or the galactic halo today motivate the computation of the neutralino annihilation cross section beyond leading order. We consider neutralino annihilation via squark exchange and parameterize the effective annihilation vertex as a dimension-six operator suppressed by two powers of the squark mass and related to the divergence of the axial vector current of the final-state quarks. Since the axial vector current is conserved at tree level in the limit of massless quarks, this dimension-six operator contains a suppression by the quark mass. The quark mass suppression can be lifted in two ways: (1) by corrections to the dimension-six operator involving the anomalous triangle diagram, and (2) by going to dimension-eight. We address the first of these possibilities by evaluating the anomalous triangle diagram, which contributes to neutralino annihilation to gluon pairs. We relate the triangle diagram via the anomaly equation to the decay of a pseudoscalar into two gluons and use the Adler–Bardeen theorem to extract the next-to-leading order (NLO) QCD corrections to χχ→gg from the known corrections to pseudoscalar decay. The strong dependence of the dominant χχ→qq¯ cross section on the relative velocity of the neutralinos makes these NLO corrections unimportant at χ decoupling but significant today.