Non-relativistic pair annihilation of nearly mass degenerate neutralinos and charginos III. Computation of the Sommerfeld enhancements
M. Beneke (Physik Department T31, Technische Universität München, James-Franck-Straße, D-85748, Garching, Germany, Institut für Theoretische Teilchenphysik und Kosmologie, RWTH Aachen University, D-52056, Aachen, Germany); C. Hellmann (Physik Department T31, Technische Universität München, James-Franck-Straße, D-85748, Garching, Germany, Institut für Theoretische Teilchenphysik und Kosmologie, RWTH Aachen University, D-52056, Aachen, Germany); P. Ruiz-Femenía (Instituto de Física Corpuscular (IFIC), CSIC-Universitat de València, Apdo. Correos 22085, E-46071, Valencia, Spain)
This paper concludes the presentation of the non-relativistic effective field theory formalism designed to calculate the radiative corrections that enhance the pair-annihilation cross sections of slowly moving neutralinos and charginos within the general minimal supersymmetric standard model (MSSM). While papers I and II focused on the computation of the tree-level annihilation rates that feed into the short-distance part, here we describe in detail the method to obtain the Sommerfeld factors that contain the enhanced long-distance corrections. This includes the computation of the potential interactions in the MSSM, which are provided in compact analytic form, and a novel solution of the multi-state Schrödinger equation that is free from the numerical instabilities generated by large mass splittings between the scattering states. Our results allow for a precise computation of the MSSM neutralino dark matter relic abundance and pair-annihilation rates in the present Universe, when Sommerfeld enhancements are important.
