Operator expansion for high-energy scattering
Ian Balitsky
TL;DR
Balitsky introduces a gauge-invariant operator expansion for high-energy QCD amplitudes using straight-line Wilson factors (Wilson lines). He demonstrates that the leading small-x logarithms arise from the evolution of these nonlocal operators with respect to the Wilson-line slope, effectively interpreting the BFKL equation as a slope-evolution equation and deriving a nonlinear extension that includes multi-pomeron interactions. The framework emphasizes a clean separation of hard and soft contributions, akin to an operator-product expansion for high-energy amplitudes. This nonlinear Wilson-line evolution provides a path toward a gauge-invariant, unitary description of high-energy scattering and the interplay between hard and soft pomeron dynamics.
Abstract
I demonstrate that the leading logarithms for high-energy scattering can be obtained as a result of evolution of the nonlocal operators - straight-line ordered gauge factors - with respect to the slope of the straight line.