Hot news on the phase-structure of the SMEFT

We perform dimensional reduction of the electroweak sector of the dimension-six SMEFT to order $g^4$ 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 $|\phi|^6$ at zero temperature, where $\phi$ is the Higgs doublet. This opens the door to entirely unexplored directions in model building.