NLO thermal corrections to dark matter annihilation cross sections: A novel approach

Dark matter relic density has been increasingly accurately measured by successive generations of experiments. The Boltzmann equation determines the yields using the dark matter annihilation cross section as one of the inputs; the accurate computation of the latter including thermal contributions thus assumes importance. We report here the next-to-leading-order (NLO) thermal corrections to the cross sections for (Majorana) dark matter annihilation of standard model fermions, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>χ</a:mi><a:mi>χ</a:mi><a:mo stretchy="false">→</a:mo><a:mi>f</a:mi><a:mover accent="true"><a:mi>f</a:mi><a:mo stretchy="false">¯</a:mo></a:mover></a:math>, via charged scalars. We use a novel approach, utilizing the technique of Grammer and Yennie, extended to thermal field theories, where the cancellation of soft infrared divergences occurs naturally. We present the NLO thermal cross sections in full detail both for the relativistic case and in the nonrelativistic limit. Our independent calculation verifies earlier results where the leading contribution at order <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mi mathvariant="script">O</f:mi><f:mo stretchy="false">(</f:mo><f:msup><f:mi>T</f:mi><f:mn>2</f:mn></f:msup><f:mo stretchy="false">)</f:mo></f:math> was shown to be proportional to the square of the fermion mass in the nonrelativistic limit, just as at leading order. We find that the <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi mathvariant="script">O</k:mi><k:mo stretchy="false">(</k:mo><k:msup><k:mi>T</k:mi><k:mn>4</k:mn></k:msup><k:mo stretchy="false">)</k:mo></k:math> contributions have the same dependence on the fermion mass as well.