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Symmetry, Vol. 15, Pages 414: How to Determine the Branch Points of Correlation Functions in Euclidean Space II: Three-Point Functions
Symmetry doi: 10.3390/sym15020414
Authors: Markus Q. Huber Wolfgang J. Kern Reinhard Alkofer
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.
