Light-by-light scattering in Double-Logarithmic Approximation

TL;DR

This paper derives explicit expressions for light-by-light scattering amplitudes at high energies in QCD, revealing a new double-logarithmic Pomeron contribution that is comparable to the BFKL Pomeron, and discusses its phenomenological relevance.

Contribution

It introduces a double-logarithmic Pomeron contribution to light-by-light scattering, providing explicit high-energy asymptotics and comparing it to the BFKL Pomeron.

Findings

The DL Pomeron has the same order contribution as the BFKL Pomeron.

Explicit expressions for scattering amplitudes in DLA are obtained.

The DL Pomeron can be relevant in certain high-energy regimes.

Abstract

In the present paper we consider the elastic 2 -> 2 -scattering of virtual photons at high energies in the forward kinematics at zero and non-zero values of t. Accounting for both gluon and quark double-logarithmic (DL) contributions to all orders in the QCD coupling, we obtain explicit expressions for amplitudes of this process in Double-Logarithmic Approximation (DLA). First we keep the QCD coupling fixed and then account for running coupling effects. Applying the saddle-point method to the obtained expressions for the scattering amplitude, we calculate the high-energy asymptotics of the amplitude, which proved to be of the Regge form. The Reggeon bears the vacuum quantum numbers and therefore it is a new, DL contribution to Pomeron. Comparison of the DL Pomeron to the BFKL Pomeron shows that contribution of the DL Pomeron to the high-energy asymptotics is of the same order as contribution of the BFKL Pomeron, so the DL Pomeron should be taken into account together with the BFKL Pomeron. We estimate the applicability region for the asymptotics of the light-by-light scattering amplitude, where the the DL Pomeron can reliably represent the parent amplitude.