Universality of 1/Q corrections revisited

TL;DR

This paper provides an exact two-loop analytical calculation of the leading power correction for the C parameter in e+e- annihilation, confirming a proportionality with the longitudinal cross section and discussing extensions to other variables.

Contribution

It offers a precise two-loop abelian calculation of power corrections for the C parameter and verifies a proportionality with the longitudinal cross section, extending understanding of event shape corrections.

Findings

Exact two-loop calculation of power correction for C parameter

Verification of proportionality between corrections to C parameter and longitudinal cross section

Discussion on extending techniques to non-abelian contributions and other variables

Abstract

We provide an exact analytical calculation at the two-loop level in the abelian limit of the leading power correction for the C parameter in e+e- annihilation. We compare our results to the numerical value obtained employing the soft approximation, the abelian part of the Milan factor. We demonstrate that a simple proportionality holds between the leading power corrections to the C parameter and to the longitudinal cross section in the soft region, and we verify that this proportionality holds for the full two-loop abelian contribution computed here. We comment on the possibility of extending this technique to other event shape variables and distributions, as well as to the non-abelian contributions.