On the quark propagator singularity

TL;DR

This paper investigates the analytic structure of the quark propagator, demonstrating that a simple pole on the real axis is incompatible with the Euclidean solutions extended to the timelike region, due to a discontinuity in the mass function.

Contribution

It applies the Fukuda and Kugo continuation method to show the absence of a simple pole in the quark propagator, challenging previous assumptions.

Findings

No simple pole in the quark propagator on the real axis

Discontinuity in the quark mass function prevents pole existence

Euclidean solutions extended to timelike momenta reveal complex structure

Abstract

Using the method of Fukuda and Kugo \cite{FUKKUG} the continuation of Euclidean solution is performed to the timelike axis of fourmomenta. It is shown that assumed presence of the real simple pole in quark propagator is not in agreement with the solution. The simple pole disappears because of the discontinuity in the resulting quark mass function.