Effect of multiple Higgs fields on the phase structure of theSU(2)-Higgs model

Abstract

The $SU(2)$-Higgs model, with a single Higgs field in the fundamental representation and a quartic self-interaction, has a Higgs region and a confinement region which are analytically connected in the parameter space of the theory; these regions thus represent a single phase. The effect of multiple Higgs fields on this phase structure is examined via Monte Carlo lattice simulations. For the case of $N\ensuremath{\ge}2$ identical Higgs fields, there is no remaining analytic connection between the Higgs and confinement regions, at least when Lagrangian terms that directly couple different Higgs flavors are omitted. An explanation of this result in terms of enhancement from overlapping phase transitions is explored for $N=2$ by introducing an asymmetry in the hopping parameters of the Higgs fields. It is found that an enhancement of the phase transitions can still occur for a moderate (10%) asymmetry in the resulting hopping parameters.