Resummation with Wilson lines off the light cone

TL;DR

This paper reviews a formalism for resumming large logarithms in perturbative QCD processes using Wilson lines off the light cone, unifying various summation techniques and enabling jet substructure calculations.

Contribution

It introduces a master equation derived from Wilson line variations that reproduces known logarithm summations and extends to jet substructure analysis.

Findings

Reproduces known single- and double-logarithm summations.

Derives a master equation for resummation formalism.

Enables calculation of jet substructures.

Abstract

I review the resummation formalism for organizing large logarithms in perturbative expansion of collinear subprocesses through the variation of Wilson lines off the light cone. A master equation is derived, which involves the evolution kernel resulting from this variation. It is then demonstrated that all the known single- and double-logarithm summations for a parton distribution function or a transverse-momentum-dependentparton distribution can be reproduced from the master equation by applying appropriate soft-gluon approximations to the evolution kernel. Moreover, jet substructures, information which is crucial for particle identification at the Large Hadron Collider and usually acquired from event generators, can also be calculated in this formalism.