Reparameterization Invariant Collinear Operators

TL;DR

This work develops a reparametrization invariant (RPI) framework within SCET by constructing RPI and gauge-invariant collinear objects and delta-function regulators that encode large momenta. By expanding RPI objects into a minimal, power-counting-friendly operator basis, the authors derive Lorentz-invariance constraints that relate Wilson coefficients across different twists and directions, enabling process-independent relations. They validate the approach by reproducing known twist-4 results in DIS for quarks and gluons and by constructing complete operator bases for multi-jet processes, including e+e- → 3 jets and gg → qq̄ in hadron collisions. The framework significantly streamlines factorization and matching for high-energy QCD with complex final states, providing a systematic path to higher-order and multi-directional jet analyses.

Abstract

In constructing collinear operators, which describe the production of energetic jets or energetic hadrons, important constraints are provided by reparameterization invariance (RPI). RPI encodes Lorentz invariance in a power expansion about a collinear direction, and connects the Wilson coefficients of operators at different orders in this expansion to all orders in alphas. We construct reparameterization invariant collinear objects. The expansion of operators built from these objects provides an efficient way of deriving RPI relations and finding a minimal basis of operators, particularly when one has an observable with multiple collinear directions and/or soft particles. Complete basis of operators are constructed for pure glue currents at twist-4, and for operators involving multiple collinear directions, including those appearing in e+e- -> 3 jets, and for pp-> 2 jets initiated via gluon-fusion.

Figures (1)

• Figure 1: Three collinear jets labeled by vectors $n_i^\mu$.