Fermionic Glauber Operators and Quark Reggeization

TL;DR

This paper develops an effective field theory framework within SCET to describe Glauber quark exchanges in the Regge limit, deriving operators, their symmetries, and their role in quark Reggeization and BFKL evolution.

Contribution

It introduces non-local fermionic potential operators for Glauber quarks in SCET, providing the first systematic derivation and analysis of their structure and effects in the Regge limit.

Findings

Derived the Glauber quark operators and their symmetry properties.

Verified the quark Regge trajectory at one-loop order.

Established the leading logarithmic BFKL equation from the theory.

Abstract

We derive, in the framework of soft-collinear effective field theory (SCET), a Lagrangian describing the $t$-channel exchange of Glauber quarks in the Regge limit. The Glauber quarks are not dynamical, but are incorporated through non-local fermionic potential operators. These operators are power suppressed in $|t|/s$ relative to those describing Glauber gluon exchange, but give the first non-vanishing contributions in the Regge limit to processes such as $q\bar q \to gg$ and $q\bar q \to \gamma \gamma$. They therefore represent an interesting subset of power corrections to study. The structure of the operators, which describe certain soft and collinear emissions to all orders through Wilson lines, is derived from the symmetries of the effective theory combined with constraints from power and mass dimension counting, as well as through explicit matching calculations. Lightcone singularities in the fermionic potentials are regulated using a rapidity regulator, whose corresponding renormalization group evolution gives rise to the Reggeization of the quark at the amplitude level and the BFKL equation at the cross section level. We verify this at one-loop, deriving the Regge trajectory of the quark in the $3$ color channel, as well as the leading logarithmic BFKL equation. Results in the $\bar 6$ and $15$ color channels are obtained by the simultaneous exchange of a Glauber quark and a Glauber gluon. SCET with quark and gluon Glauber operators therefore provides a framework to systematically study the structure of QCD amplitudes in the Regge limit, and derive constraints on higher order amplitudes.