# Interacting two-particle states in the symmetric phase of the chiral Nambu--Jona-Lasinio model

## TL;DR

This paper uses the Functional Renormalisation Group to analyze two-particle states in the symmetric phase of the chiral Nambu--Jona-Lasinio model, revealing bound state characteristics and interaction energies.

## Contribution

It introduces a non-local effective action approach to study two-particle states and their bound state interpretation within the NJL model using FRG.

## Key findings

- Identification of non-zero limiting composite couplings for two-particle states
- Extraction of negative interaction energy as a function of composite size
- Bound state interpretation of minimal interaction energy states

## Abstract

The renormalisation group flow of the chiral Nambu--Jona-Lasinio (NJL) model with one fermion flavor is mapped out in the symmetric phase with the help of the Functional Renormalisation Group (FRG) method using a physically motivated non-local trial effective action. The well-known infrared unstable strongly coupled fixed point characterized by a set of pointlike four-fermion couplings is reproduced. The Gaussian infrared end-point of the flow of the four-fermion couplings is now accompanied by non-zero limiting composite couplings characteristic for interacting two-particle states with finite energy and physical size. The negative interaction energy of the constituents is extracted as a function of the physical size of the composite object. This function reaches a minimum in the accessible range of physical sizes, mildly depending on the set of initial values of the couplings. The propagation of a two-particle state minimizing the interaction energy has a natural bound state interpretation.