Four-quark scatterings in QCD I

TL;DR

This paper uses the functional renormalisation group to analyze four-quark interactions in QCD, revealing how chiral symmetry breaking and meson formation emerge from scalar-pseudoscalar channels.

Contribution

It provides a Fierz-complete fRG analysis of four-quark interactions, connecting the dynamics to Bethe-Salpeter and gap equations, including momentum dependence and Minkowski regime calculations.

Findings

Identified the scalar-pseudoscalar channel as key to chiral symmetry breaking.

Computed the pion pole mass from Minkowski and Euclidean analyses, finding consistent results.

Abstract

We investigate dynamical chiral symmetry breaking and the emergence of mesonic bound states from the infrared dynamics of four-quark scatterings. Both phenomena originate from the resonant scalar-pseudoscalar channel of the four-quark scatterings, and we compute the functional renormalisation group (fRG) flows of the Fierz-complete four-quark interaction of up and down quarks with its $t$ channel momentum dependence. This is done in the isospin symmetric case, also including the flow of the quark two-point function. This system can be understood as the fRG analogues of the complete Bethe-Salpeter equations and quark gap equation. The pole mass of the pion is determined from both direct calculations of the four-quark flows in the Minkowski regime of momenta and the analytic continuation based on results in the Euclidean regime, which are consistent with each other.