Minkowski space structure of the Higgs potential in 2HDM: II. Minima, symmetries, and topology

TL;DR

This paper analyzes the vacuum structure of the two-Higgs-doublet model using Minkowski space geometry, establishing limits on minima, symmetry breaking, and topological features of the potential.

Contribution

It introduces a Minkowski space framework to study Higgs potential minima, symmetries, and topology in 2HDM, providing new criteria and insights.

Findings

2HDM cannot have more than two local minima.

A twice-degenerate minimum arises only via spontaneous symmetry breaking.

Criteria for non-contractible paths in Higgs orbit space are established.

Abstract

We continue to explore the consequences of the recently discovered Minkowski space structure of the Higgs potential in the two-Higgs-doublet model. Here, we focus on the vacuum properties. The search for extrema of the Higgs potential is reformulated in terms of 3-quadrics in the 3+1-dimensional Minkowski space. We prove that 2HDM cannot have more than two local minima in the orbit space and that a twice-degenerate minimum can arise only via spontaneous violation of a discrete symmetry of the Higgs potential. Investigating topology of the 3-quadrics, we give concise criteria for existence of non-contractible paths in the Higgs orbit space. We also study explicit symmetries of the Higgs potential/lagrangian and their spontaneous violation from a wider perspective than usual.