How to determine the branch points of correlation functions in Euclidean space II: Three-point functions

TL;DR

This paper discusses a method to analyze the analytic structure of three-point correlation functions in quantum field theory, crucial for understanding bound states and spectra in quantum chromodynamics, using contour deformation techniques.

Contribution

It introduces a contour deformation method for three-point functions applicable to complex theories like QCD, enhancing the analysis of their analytic structure.

Findings

Method applicable to scalar and more complex theories

Facilitates inclusion in truncation schemes for QCD

Aids in calculating bound state spectra

Abstract

The analytic structure of elementary correlation functions of a quantum field is relevant for the calculation of masses of bound states and their time-like properties in general. In quantum chromodynamics, the calculation of correlation functions for purely space-like momenta has reached a high level of sophistication, but the calculation at time-like momenta requires refined methods. One of them is the contour deformation method. Here we describe how to employ it for three-point functions. The basic mechanisms are discussed for a scalar theory, but they are the same for more complicated theories and are thus relevant, e.g., for the three-gluon or quark-gluon vertices of quantum chromodynamics. Their inclusion in existing truncation schemes is a crucial step for investigating the analytic structure of elementary correlation functions of quantum chromodynamics and the calculation of its spectrum from them.