Cosmological abundances of electroweak Dark Matter models for future high-energy colliders

The simplest extension to the Standard Model (SM) which can accommodate a Dark Matter (DM) candidate consists of a single additional $SU(2)_L$ $n-$plet with 0 or milli-hypercharge. We require odd $n$ in order to evade direct detection constraints and $n\leq 7$ to avoid electroweak Landau poles too close to the DM mass. In view of a possible future high-energy lepton collider, it is of prominent importance to precisely determine the DM mass required to reproduce the observed cosmological abundance. Such a computation relies on the precise determination of the DM annihilation cross-section, which includes non-perturbative effects like the Sommerfeld enhancement and especially the bound states formation. Up-to-date, a precise prediction of the DM mass is available only for the triplets and the Majorana 5-plet (A. Mitridate et al., JCAP, 05 (2017)). We refine and extend these computations in order to encompass all the $n-$plets up to $n=7$. For such large electroweak charges the non-perturbative effects are enhanced, and push the predicted DM mass to tens of TeV. In particular, we find a thermal mass of 36 TeV and 44 TeV for Complex Scalar and Majorana 7-plets, respectively. These could both be probed at a multi-TeV muon collider.