Factorization and high-energy effective action

TL;DR

This work proposes a factorization of high-energy QCD scattering in rapidity space, separating fast and slow field contributions via Wilson-line operators along a rapidity divide. By merging operator expansions with a two-step factorization, Balitsky defines a high-energy effective action S_eff that encodes the physics of a given rapidity interval and generates leading-log BFKL dynamics through its perturbative expansion. The framework is developed both in a general functional-integral form and in a semiclassical treatment of colliding shock waves, illustrating how Lipatov’s reggeization and the BFKL kernel emerge within this effective-action approach. The methodology sets the stage for a potentially nonperturbative, two-dimensional describing theory for high-energy QCD processes and provides a path toward unitarization of the BFKL pomeron.

Abstract

I demonstrate that the amplitude for high-energy scattering can be factorized as a convolution of the contributions due to fast and slow fields. The fast and slow fields interact by means of Wilson-line operators -- infinite gauge factors ordered along the straight line. The resulting factorization formula gives a starting point for a new approach to the effective action for high-energy scattering in QCD.

Figures (13)

• Figure 1: Structure of the factorization formula. Dashed, solid, and wavy lines denote photons, quarks, and gluons, respectively. Wilson-line operators are denoted by dotted lines and the vector $n$ gives the direction of the "rapidity divide" between fast and slow fields.
• Figure 2: The effective action for the interval of rapidities $\eta_0>\eta>\eta'_0$. The two vectors $n$ and $n'$ correspond to "rapidity divides" $\eta_0$ and $\eta'_0$ bordering our chosen region of rapidities
• Figure 3: Quark propagator in a shock-wave background
• Figure 4: A typical Feynman diagram for the $\gamma^*\gamma^*$ scattering amplitude (a) and the corresponding two-Wilson-line operator (b)
• Figure 5: Decomposition into product of coefficient function and matrix element of the two-Wilson-line operator for a typical Feynman diagram. (Double Wilson line corresponds to fast-moving gluon)