Asymptotic Limits and Sum Rules for the Quark Propagator

TL;DR

This paper investigates the asymptotic behavior of the quark propagator's structure functions across different gauges and directions, deriving sum rules and highlighting gauge independence of leading terms under asymptotic freedom.

Contribution

It provides a comprehensive analysis of the quark propagator's asymptotics in covariant gauges, extending previous gauge field results and establishing gauge-independent leading terms and sum rules.

Findings

Asymptotic behavior is characterized for all directions in the complex $k^2$-plane.

Leading terms are determined by one- or two-loop calculations and are gauge independent.

Derived sum rules relate the structure functions and their asymptotics.

Abstract

For the structure functions of the quark propagator, the asymptotic behavior is obtained for general, linear, covariant gauges, and in all directions of the complex $k^2$-plane. Asymptotic freedom is assumed. Corresponding previous results for the gauge field propagator are important in the derivation. Except for coefficients, the leading asymptotic terms are determined by one-loop or by two-loop information, and are gauge independent. Various sum rules are derived.