Colour Evolution and Infrared Physics

TL;DR

This paper develops a detailed formalism for soft gluon and massless quark evolution in colour space, connecting it to infrared subtraction techniques and observable structures, with implications for non-global observables and power corrections.

Contribution

It provides a comprehensive two-loop level formalism for colour evolution equations, linking them to infrared subtractions and observable-dependent measurements.

Findings

Evolution kernels relate to infrared subtractions.

The formalism applies to energy ordering and angular cutoffs.

Insights into soft gluon effects on power corrections.

Abstract

We give a complete account of how soft gluon, massless quark, evolution equations in colour space originate, from a factorization into a hard cross section density operator and a soft function encoding measurements and the projection on definite colours. We detail this formalism up to the two loop level and we demonstrate how the evolution kernels relate to infrared subtractions, and how the resolution of infrared singular regions conspires with the structure of observables the algorithm should be able to predict. The latter allows us to address evolution in different kinematic variables, including energy ordering and angular cutoffs in non-global observables. The soft factor and its evolution resembles a hadronization model including effects such as colour reconnection, and could give insight into the structure of power corrections in observables which require soft gluon evolution.