Quark-gluon backscattering in the Regge limit at one-loop

Abstract

At small momentum transfer, the quark-gluon scattering cross section dσ/dt has a power-law divergence in the backward scattering region where the outgoing quark is nearly collinear to the incoming gluon. In this Regge limit |t| ≪ s, the leading behavior of the 2 → 2 amplitude can be described by the exchange of Glauber quarks. In Soft-Collinear Effective Theory (SCET) at leading power, Glauber quark exchange is given by five non-local Glauber quark operators, of which only one is generated at tree-level. We show that at leading power the QCD amplitude for quark-gluon backscattering at one-loop can be exactly reproduced by SCET using the tree-level Glauber operator. The agreement between QCD and SCET of the ultraviolet, infrared, and rapidity divergences as well as all logarithms, Glauber phases and finite parts for all polarizations of the external gluons is a strong check on the effective theory. We find that the entire one-loop matching vanishes — there is no correction to the operator generated at tree-level, and the coefficients of the other four operators remain zero at one-loop. This suggests that SCET with Glauber operators may be useful for uncovering new aspects of Regge physics in a systematically improvable way.

Anomalous dimensions from soft Regge constants

“…There are many directions for future study. Using an identical approach combined with the Glauber quark operators [60] (see [71] for a verification of these operators at one-loop order), one should be able to give a simple direct calculation of the two-loop quark Regge trajectory in QCD/QED, which has so far only be derived from direct expansion of the two loop amplitudes [72]. Also at the two-loop level, it would be interesting to understand possible iterative structures in other color channels, for example the pomeron.…”

Snowmass 2021 White Paper: Resummation for future colliders

“…Further progress will require a better understanding of the renormalization properties of these complicated non-local objects. Beyond the applications of SCET I that are discussed here, there are new interesting areas of study in SCET II involving subleading power rapidity divergences for transverse momentum distributions [49], Energy-Energy correlators [110], Regge kinematics and forward scattering [111,112], and azimuthal asymmetries in semi-inclusive deep inelastic scattering [113].…”