Saddle-point method for resummed form factors in QCD

TL;DR

This paper introduces an analytic saddle-point method for inverting QCD form factors in event shape resummation, providing accurate results that improve upon classical Taylor expansion approaches.

Contribution

It develops a novel saddle-point based analytic formula for the inverse transform of QCD resummed form factors, enhancing precision over traditional methods.

Findings

The saddle-point method agrees well with numerical inverse transforms.

It significantly differs from classical Taylor expansion approaches.

The approach improves the accuracy of resummation in momentum space.

Abstract

We consider the form factor appearing in QCD resummation formalism for event shape distributions in the two-jet (or Sudakov) region. We present an analytic formula for the inverse transform of the form factor, namely from the conjugate moment space to the (physical) momentum space, based on the saddle-point method. The saddle-point itself is determined by means of an analytic recursion method as well as by standard numerical methods. The results we have found are in very good agreement with the exact (numerical) evaluation of the inverse transform, while they significantly differ from classical analytical formulations of resummation in momentum space. The latter are based on a Taylor expansion of the form factor around the free-theory saddle point.