Renormalisation of heavy-light light ray operators

TL;DR

This paper computes the renormalisation of heavy-light light ray operators, revealing how conformal symmetry is broken at one loop and providing insights into operator mixing and renormalisation kernels.

Contribution

It presents the first detailed calculation of renormalisation kernels for heavy-light light ray operators, including mixing with three-particle operators and the impact of cusp renormalisation.

Findings

Light degrees of freedom govern operator mixing with three-particle operators.

Conformal symmetry is broken at one loop due to cusp renormalisation.

Results enable fixing of renormalisation kernels up to a constant.

Abstract

We calculate the renormalisation of different light ray operators with one light degree of freedom and a static heavy quark. Both $2\to2$- and $2\to3$-kernels are considered. A comparison with the light-light case suggests that the mixing with three-particle operators is solely governed by the light degrees of freedom. Additionally we show that conformal symmetry is already broken at the level of the one loop counterterms due to the additional UV-renormalisation of a cusp in the two contributing Wilson-lines. This general feature can be used to fix the $2\to2$-renormalisation kernels up to a constant. Some examples for applications of our results are given.