Quark-Gluon Backscattering in the Regge Limit at One-Loop

TL;DR

This paper demonstrates that Soft-Collinear Effective Theory with Glauber quark operators accurately reproduces the one-loop quark-gluon backscattering amplitude in the Regge limit, confirming the theory's consistency and potential for further insights.

Contribution

The work shows that at one-loop, the SCET Glauber operator matches the QCD amplitude exactly, with no additional corrections, highlighting the theory's robustness in Regge physics.

Findings

Exact reproduction of one-loop amplitude by SCET Glauber operator

No one-loop corrections to the Glauber operator coefficients

Strong agreement between QCD and SCET divergences and finite parts

Abstract

At small momentum transfer, the quark-gluon scattering cross section d{\sigma}/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 improveable way.