# Singularity Free Direct Calculation of Spontaneous Mass Generation

## TL;DR

This paper introduces a novel iterative regularization method for directly calculating spontaneous mass generation in quantum field theories, avoiding singularities and additional assumptions, with some limitations in first-order phase transitions.

## Contribution

The paper presents a new iterative approach that reliably computes dynamical mass without singularities, applicable to models with chiral symmetry breaking.

## Key findings

- Successfully computes physical mass in NJL and gauge theories
- Avoids singularities and free energy comparisons
- Potential issues in first-order phase transitions

## Abstract

We propose a new iterative method to directly calculate the spontaneous mass generation. It is regarded as a new regularization method resembling the finite volume calculation which assures non-negative fluctuation property at every stage. We work with the Nambu--Jona-Lasinio model and the strong coupling gauge theory where the dynamical chiral symmetry breaking occurs. We are able to conclude the physical mass definitely without encountering any singularity nor recourse to any additional consideration like the free energy comparison. However in special case of the 1st order phase transition, we find that the iterative method has a chance to go wrong.