Electroweak phase transition in the $\Sigma$SM - I: Dimensional reduction

TL;DR

This paper develops a high-temperature effective theory for the $\\Sigma$SM to facilitate lattice simulations of the electroweak phase transition, comparing non-perturbative results with conventional perturbation theory.

Contribution

It derives a dimensionally reduced effective theory for the $\\Sigma$SM suitable for lattice simulations and maps the phase diagram, highlighting regions with different phase transition types.

Findings

Effective theory matches minimal Standard Model form when $\\Sigma$ is heavy.

Phase diagram shows regions of first order, second order, and crossover transitions.

Prospects for collider measurements to probe first order transition regions.

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 Standard Model ($\Sigma$SM). In Part I (this paper), we derive and present the high-$T$ dimensionally reduced effective theory that is suitable for numerical simulation on the lattice. In the sequel (Part II), we will present results of the numerical simulation and benchmark the performance of conventional perturbation theory. Under the assumption that $\Sigma$ is heavy, the resulting effective theory takes the same form as that derived from the minimal standard model. By recasting the existing non-perturbative results, we map out the phase diagram of the model in the plane of triplet mass $M_\Sigma$ and Higgs portal coupling $a_2$. Contrary to conventional perturbation theory, we find regions of parameter space where 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 $h\rightarrow\gamma\gamma$ partial width.