Asymptotic Limits and Sum Rules for Gauge Field Propagators

TL;DR

This paper derives the asymptotic behavior of gauge field propagators across the complex plane in various gauges, establishing gauge-independent forms and sum rules that extend previous superconvergence relations, with exact exponents from one-loop calculations.

Contribution

It provides a comprehensive analysis of the asymptotic limits of gauge propagators in all directions and gauges, introducing generalized sum rules beyond the Landau gauge.

Findings

Asymptotic forms are gauge-independent except for coefficients.

Exponents are exactly determined by one-loop calculations.

Generalized sum rules extend superconvergence relations.

Abstract

For gauge field propagators, the asymptotic behavior is obtained in all directions of the complex $k^2$-plane, and for general, linear, covariant gauges. Asymptotically free theories are considered. Except for coefficients, the functional form of the leading asymptotic terms is gauge-independent. Exponents are determined exactly by one-loop expressions. Sum rules are derived, which generalize the superconvergence relations obtained in the Landau gauge. (To appear in Physics Letters B)