Hadronic bound-states in SU(2) from Dyson--Schwinger Equations

TL;DR

This paper calculates the spectrum of hadrons in an SU(2) gauge theory using Dyson-Schwinger equations, highlighting the limitations of the rainbow-ladder approximation and proposing a more sophisticated truncation method that aligns well with lattice results.

Contribution

The study introduces a refined truncation approach for Dyson-Schwinger equations in SU(2) theories, improving upon the rainbow-ladder approximation for accurate hadron spectrum predictions.

Findings

Rainbow-ladder truncation is inadequate for SU(2) theories.

A new truncation at the quark-gluon vertex level yields results consistent with lattice data.

Highlights the importance of advanced techniques for strongly interacting gauge theories.

Abstract

By using the Dyson-Schwinger/Bethe-Salpeter formalism in Euclidean spacetime, we calculate the ground state spectrum of $J\leq 1$ hadrons in an SU(2) gauge theory with 2 fundamental fermions. We show that the rainbow-ladder truncation, commonly employed in QCD studies, is unsuitable for a description of an SU(2) theory. This we remedy by truncating at the level of the quark-gluon vertex Dyson-Schwinger equation in a diagrammatic expansion. Results obtained within this novel approach show good agreement with lattice studies. These findings emphasize the need to use techniques more sophisticated than rainbow-ladder when investigating generic strongly interacting gauge theories.