Gauge invariance and the physical spectrum in the two-Higgs-doublet model

TL;DR

This paper explores the gauge-invariant physical spectrum in the two-Higgs-doublet model, relating it to elementary particles and considering symmetry breaking, with implications for lattice testing methods.

Contribution

It extends the Fröhlich-Morchio-Strocchi mechanism to the two-Higgs-doublet model and analyzes the impact of global symmetry breaking on the physical spectrum.

Findings

Relation between gauge-invariant states and elementary particles established

Effects of spontaneous global symmetry breaking analyzed

Guidelines for lattice testing of the spectrum provided

Abstract

Observable states are gauge-invariant. In a non-Abelian gauge theory, these are necessarily composite operators. We investigate the spectrum of these operators in the two-Higgs-doublet model. For this purpose, we are working along the lines of the Fr\"ohlich-Morchio-Strocchi mechanism to relate the physical spectrum to the spectrum of the elementary particles. We also investigate the consequences of spontaneous breaking of the global (custodial) symmetry group. Finally, we briefly comment on how to test the results using lattice methods.