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This paper concludes the presentation of the non-relativistic effective field theory formalism designed to calculate the radiative corrections that enhance the pairannihilation 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.

We present a systematic procedure to obtain the one-loop low-energy effective Lagrangian resulting from integrating out the heavy fields of a given ultraviolet theory. We show that the matching coefficients are determined entirely by the hard region of the functional determinant involving the heavy fields. This represents an important simplification with respect the conventional matching approach, where the full and effective theory contributions have to be computed separately and a cancellation of the infrared divergent parts has to take place. We illustrate the method with a descriptive toy model and with an extension of the Standard Model with a heavy real scalar triplet. A comparison with other schemes that have been put forward recently is also provided.

We analyse subleading electroweak effects in the top anti-top resonance production region in e + e − collisions which arise due to the decay of the top and anti-top quarks into the W + W − bb final state. These are NLO corrections adopting the nonrelativistic power counting v ∼ α s ∼ √ α EW . In contrast to the QCD corrections which have been calculated (almost) up to NNNLO, the parametrically larger NLO electroweak contributions have not been completely known so far, but are mandatory for the required accuracy at a future linear collider. The missing parts of these NLO contributions arise from matching coefficients of non-resonant productiondecay operators in unstable-particle effective theory which correspond to off-shell top production and decay and other non-resonant irreducible background processes to tt production. We consider the total cross section of the e + e − → W + W − bb process and additionally implement cuts on the invariant masses of the W + b and W −b pairs.