Colour evolution and infrared physics

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.

Precision QCD at FCC-ee

“…Building blocks for higher order evolution start to become available, see for instance in [22][23][24][25], however constructing a functional algorithm which would leverage these building blocks to improve on shower accuracy is a largely complicated endeavor so far not achieved, with some structures only highlighted recently [26][27][28]. Specifically in the soft evolution, progress has been made to identify the structure of evolution equations for soft parton showers at and even beyond the large-𝑁 limit [27,29], and there are exploratory steps within other parton showers [30]. However, beyond leading colour, the probabilistic interpretation of parton showers is lost.…”

“…The factorization at the parton shower infrared cutoff is a central point in constructing parton shower algorithms and constraining hadronization models. We have been studying the cutoff dependence in [32] in connection to power corrections in event shapes and the top quark mass parameter, and also have exploited this fact in [27] to construct entire evolution equations for a parton shower algorithm and a soft factor which would be able to describe hadronization. This has up until now happened in the soft gluon case, though with obvious generalizations beyond this.…”