Hot news on the phase-structure of the SMEFT

We perform dimensional reduction of the electroweak sector of the dimension-six SMEFT to order g⁴ in coupling constants g. This analysis includes one-loop contributions to kinetic terms and quartic couplings; as well as two-loop contributions, where operators such as four-fermion interactions first appear, to squared mass terms. Using lattice data, we also provide evidence that, in contrast with previous statements in the literature, the SMEFT may undergo a first-order phase transition even for null |ϕ|⁶ at zero temperature, where $ϕ$ is the Higgs doublet. This opens the door to entirely unexplored directions in model building.