Reparameterization Invariant Collinear Operators

TL;DR

This paper develops reparameterization invariant collinear operators to efficiently derive relations and construct minimal bases for jet production processes, ensuring Lorentz invariance in effective field theories.

Contribution

It introduces reparameterization invariant objects and constructs a complete basis of operators for complex jet processes at higher twist levels.

Findings

Constructed a complete basis for pure glue currents at twist-4.

Derived RPI relations for operators with multiple collinear directions.

Facilitated analysis of jet production in e+e- and proton-proton collisions.

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.