All-loop four-quark Bethe-Salpeter kernel

Piotr Bargiela

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arXiv · 2605.05349

All-loop four-quark Bethe-Salpeter kernel

Piotr Bargiela

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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.

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Piotr Bargiela. 2026-05-06. All-loop four-quark Bethe-Salpeter kernel. https://arxiv.org/abs/2605.05349

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