High-Energy Amplitudes in Gauge Theories in the Next-to-Leading-Order

Abstract

Scattering processes play a central role in physics, and high-energies experiments give us an insight into the fine structure of matter. The high-energy behavior of amplitudes in gauge theories can be reformulated in terms of the evolution of Wilson-line operators. In the leading order this evolution is governed by the non-linear Balitsky-Kovchegov (BK) equation. In order to see if this equation is relevant for existing or future deep inelastic scattering (DIS) accelerators (like Electron Ion Collider (EIC) or Large Hadron electron Collider (LHeC)) one needs to know how large are the next-to-leading order (NLO) corrections. In addition, the NLO corrections define the scale of the running-coupling constant in the BK equation and therefore determine the magnitude of the leading-order cross sections. The first main result of this thesis is the calculation of these NLO corrections. In Quantum Chromodynamics (QCD), the next-to-leading order BK equation has both conformal and non-conformal parts. To separate the conformally invariant effects from the running-coupling effects, we first restore the conformal NLO BFKL kernel out of the eigenvalues known from the forward NLO BFKL result using the requirement of Mobius invariance of N=4 SYM amplitudes in the Regge limit, and then we calculate the NLO evolution of the color dipoles in the conformal N=4 SYM theory. To this end we define the dipole with the rapidity cutoff preserving conformal invariance, and the resulting Mobius invariant kernel for this operator agrees with the forward NLO BFKL calculation of Ref. [47]. In QCD, the NLO kernel for the composite operators resolves in a sum of the conformal part and the running-coupling part