Scattering amplitudes of proton-Nucleus or Nucleus-Nucleus collisions
at high-energy are described by matrix elements of Wilson line operators.
The energy dependence of such amplitudes is obtained by the evolution equation of Wilson
lines with respect to the rapidity of the scattering particles - Balitsky-hierarchy of non-linear evolution equations.
Most of the current phenomenology of high-energy and high-density QCD is based on the
leading-order evolution equation with only running coupling corrections.
I will present the derivation of the Wilson lines evolution equation at the next-to-leading order
using the background shock-wave formalism and the high-energy Operator Product Expansion.