Electroweak phase transition in the real triplet extension of the SM: Dimensional reduction

Abstract

In a series of two papers, we make a comparative analysis of the performance of conventional perturbation theory to analyze electroweak phase transition in the real triplet extension of the Standard Model ($\mathrm{\ensuremath{\Sigma}}\mathrm{SM}$). In Part I (this paper), we derive and present the $\mathrm{high}\text{\ensuremath{-}}T$ dimensionally reduced effective theory that is suitable for numerical simulation on the lattice. In Part II, we will present results of the numerical simulation and benchmark the performance of conventional perturbation theory. Under the assumption that $\mathrm{\ensuremath{\Sigma}}$ is heavy, the resulting effective theory takes the same form as that derived from the minimal Standard Model. By recasting the existing nonperturbative results, we map out the phase diagram of the model in the plane of triplet mass ${M}_{\mathrm{\ensuremath{\Sigma}}}$ and Higgs portal coupling ${a}_{2}$. Contrary to conventional perturbation theory, we find regions of parameter space in which the phase transition may be first order, second order, or crossover. We comment on prospects for prospective future colliders to probe the region where the electroweak phase transition is first order by a precise measurement of the $h\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}$ partial width.