Dynamical mass generation by source inversion: calculating the mass gap of the chiral Gross-Neveu model

TL;DR

This paper introduces a non-perturbative method to calculate the mass gap in the chiral Gross-Neveu model by using source inversion and scheme-invariant quantities, providing accurate results for N>2.

Contribution

It develops a scheme and scale invariant approach to determine the mass gap via source inversion, improving non-perturbative calculations in the model.

Findings

Derived an expression for the invariant source $ ilde{J}$ as a function of the mass gap.

Obtained a non-perturbative mass gap solution by setting $ ilde{J}=0$.

Achieved good agreement with expected results for N>2.

Abstract

We probe the U(N) chiral Gross-Neveu model with a source-term $J\l{\Psi}\Psi$. We find an expression for the renormalization scheme and scale invariant source $\hat{J}$, as a function of the generated mass gap. The expansion of this function is organized in such a way that all scheme and scale dependence is reduced to one single parameter $d$. We obtain a non-perturbative mass gap as the solution of $\hat{J}=0$. A physical choice for $d$ gives good results for $N>2$. The self-consistent minimal sensitivity condition gives a slight improvement.