Mesonic Wavefunctions in the three-dimensional Gross-Neveu model

TL;DR

This study numerically investigates mesonic wavefunctions in the (2+1)-dimensional Gross-Neveu model, revealing how interaction strength and temperature affect bound states, scattering, and screening phenomena.

Contribution

It provides the first detailed numerical analysis of mesonic wavefunctions across different phases in the 3D Gross-Neveu model, including temperature effects.

Findings

Wavefunctions reveal interaction effects more clearly than spectroscopy in the strongly coupled phase.

Fermion-antifermion scattering information is obtained in the weakly coupled phase.

Evidence of screened interactions is found in the hot chirally restored phase.

Abstract

We present results from a numerical study of bound state wavefunctions in the (2+1)-dimensional Gross-Neveu model with staggered lattice fermions at both zero and nonzero temperature. Mesonic channels with varying quantum numbers are identified and analysed. In the strongly coupled chirally broken phase at T=0 the wavefunctions expose effects due to varying the interaction strength more effectively than straightforward spectroscopy. In the weakly coupled chirally restored phase information on fermion - antifermion scattering is recovered. In the hot chirally restored phase we find evidence for a screened interaction. The T=0 chirally symmetric phase is most readily distinguished from the symmetric phase at high T via the fermion dispersion relation.