Medium-dependent matching conditions at higher perturbative accuracy

Determine the medium-dependent matching conditions for the soft-collinear operators, collinear functions, and their renormalization-group evolution at perturbative accuracy comparable to the known three-loop vacuum BMS evolution.

Background

The paper explains that extending the framework to higher perturbative accuracy requires calculating the soft-collinear operators, collinear functions, their renormalization-group evolution, and the medium-modified boundary conditions at the corresponding order.

Several vacuum ingredients can be imported from existing results, including vacuum BMS evolution known up to three loops. The unresolved component explicitly identified by the authors is the determination of medium-dependent matching conditions with comparable precision.