Wino potential and Sommerfeld effect at NLO

Abstract

We calculate the SU(2)×U(1) electroweak static potential between a fermionic triplet in the broken phase of the Standard Model in the one-loop order (NLO). The one-loop correction provides the leading non-relativistic correction to the large Sommerfeld effect in the annihilation of wino or wino-like dark matter particles χ 0 . We find sizeable modifications of the χ 0 χ 0 annihilation cross section and determine the shifts of the resonance locations due to the loop correction to the wino potential. arXiv:1909.04584v1 [hep-ph]

Sommerfeld-corrected relic abundance of wino dark matter with NLO electroweak potentials

“…In the previous letter [33], we discussed, for the first time, the Sommerfeld effect for wino DM with one-loop, next-to-leading order (NLO) corrections to the electroweak Yukawa potential. More precisely, we considered the pair annihilation of the DM particle χ 0 into γ + X, and found the NLO potential to give a sizeable correction to the LO Sommerfeld effect, including a shift of the Sommerfeld resonance positions by about 6%.…”

“…The present paper serves two purposes. First, we extend the one-loop computation to the potentials in the co-annihilation channels χ 0 χ ± , χ ± χ ± , which were not given in [33], and perform the first computation of a DM relic abundance with the NLO Sommerfeld effect. Second, we provide analytic results for the potentials in momentum space, and the technical details of the NLO computation.…”

“…First, from potentials that are more singular than 1/r, but the structure of the non-relativistic EFT vertices implies that such potentials can appear only from the next-to-next-to-leading order in the power-counting (similar to QED/QCD). Second, from the one-loop correction to the tree-level Coulomb and Yukawa potentials, which are the subject of this paper and [33].…”

“…The results for the other channels are discussed subsequently, and the differences are highlighted. In doing so, we provide technical details and analytic expressions not supplied in [33]. We further discuss the renormalization scheme, the gauge invariance of the results, the large-and small-distance asymptotic behaviour, and the top-quark mass dependence of the NLO correction.…”

“…19), the triple gauge vertex diagrams (A. These channels are sufficient for the calculation of the indirect detection cross section from χ 0 χ 0 annihilation as outlined in [33]. For the DM relic abundance computation, the charged co-annihilation channels are also needed.…”