All-loop four-quark Bethe-Salpeter kernel

TL;DR

This paper analytically computes the all-loop four-quark Bethe-Salpeter kernel in massless QCD using advanced amplitude methods, providing a systematic perturbative approach that avoids truncation ambiguities.

Contribution

It introduces a novel all-loop calculation of the four-quark Bethe-Salpeter kernel employing modern scattering amplitude techniques in the large N_f limit.

Findings

Derived the all-loop perturbative kernel in terms of Generalized Polylogarithms.

Provided results for gluon and quark propagators as a byproduct.

Outlined a pathway towards nonperturbative formulations.

Abstract

We analytically calculate the all-loop bare perturbative part of the four-quark Bethe-Salpeter kernel using modern scattering amplitude methods. We work to subleading order in the large number of quark flavors approximation of massless Quantum Chromodynamics, which simultaneously makes an all-loop calculation feasible, is systematically improvable, and preserves asymptotic freedom. It also allows for avoiding the ambiguity of choosing a truncation scheme in Dyson-Schwinger equations. We exploit state-of-the-art methods in Integration-By-Parts reduction of Lorentz scalar Feynman integrals into a minimal Master Integral basis, and direct integration into Generalized Polylogarithms. As a byproduct of our calculation, we also provide the result for the gluon and quark propagators. We discuss a path towards nonperturbative formulation and potential future phenomenological applications.