  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.
