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

TL;DR

This paper introduces a non-perturbative method to calculate the mass gap in the Gross-Neveu model using source inversion, achieving accurate results for large N by reducing scheme dependence.

Contribution

It presents a novel source-inversion approach to compute the mass gap, with a scheme and scale invariant formulation that improves accuracy over previous methods.

Findings

Non-perturbative mass gap obtained as solution of $\, ext{J}=0$

High accuracy results for N>2 using minimal sensitivity

Effective reduction of scheme dependence to a single parameter d

Abstract

We probe the U(N) Gross-Neveu model with a source-term $J\bar{\Psi}\Psi$. 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 get a non-perturbative mass gap as the solution of $\hat{J}=0$. In one loop we find that any physical choice for d gives good results for high values of N. In two loops we can determine d self-consistently by the principle of minimal sensitivity and find remarkably accurate results for N>2.