Gauss-Manin equations for propagators in the case of arbitrary masses

TL;DR

This paper derives the singularities and differential equations for propagators with arbitrary complex masses across various diagrams, advancing the understanding of their mathematical structure in quantum field theories.

Contribution

It provides a complete list of propagator singularities and closed-form differential equations for arbitrary masses and diagrams, extending previous results.

Findings

Identified all singularities of propagators with arbitrary complex masses.

Derived closed-form differential equations for propagators as functions of momentum and masses.

Applicable to arbitrary Feynman diagrams.

Abstract

We derive the complete list of singularities of propagators in theories with arbitrary (complex) masses and for arbitrary diagram. We derive in a closed form differential equations for the propagator as a function of the momentum and masses.