Four fermion operators and the search for BSM Physics

TL;DR

This study uses Monte Carlo simulations to explore the phase structure of an SU(2) gauge theory with four fermion operators, revealing different phase transition behaviors depending on gauge coupling strength.

Contribution

It provides the first detailed lattice investigation of the interplay between four fermion interactions and gauge dynamics in SU(2) theories.

Findings

Crossover in chiral condensate at strong four fermion coupling

Continuous phase transition at weak gauge coupling

First order phase transition at strong gauge coupling with confinement

Abstract

We report on Monte Carlo simulations focused on elucidating the phase structure of a SU(2) gauge theory containing $N_f$ Dirac fermion flavors transforming in the fundamental representation of the group and interacting through an additional chirally invariant four fermion term. Pairs of physical flavors are implemented using the two tastes present in a reduced staggered fermion formulation of the theory with the Yukawa interactions necessary for generating the four fermion term preserving the usual shift symmetries. We observe a crossover in the behavior of the chiral condensate for strong four fermi coupling associated with the generation of a dynamical mass for the fermions. At weak gauge coupling this crossover is consistent with the usual continuous phase transition seen in the pure (ungauged) NJL model. However, if the gauge coupling is strong enough to cause confinement we observe a much more rapid crossover in the chiral condensate consistent with a first order phase transition.