Operator Constraints for Twist-3 Functions and Lorentz Invariance Properties of Twist-3 Observables

TL;DR

This paper explores how Lorentz invariance relations (LIRs) can eliminate frame dependence in twist-3 functions, ensuring consistent descriptions of transverse spin observables in high-energy hadron production.

Contribution

It derives new Lorentz invariance relations for twist-3 fragmentation functions, extending previous distribution function results, and demonstrates their role in frame-independent analysis.

Findings

LIRs remove lightcone vector dependence in twist-3 functions

Twist-3 observables can be expressed using only three-parton correlations

Frame dependence in perturbative coefficient functions can be eliminated using LIRs

Abstract

We investigate the behavior under Lorentz tranformations of perturbative coefficient functions in a collinear twist-3 formalism relevant for high-energy observables including transverse polarization of hadrons. We argue that those perturbative coefficient functions can, {\it a priori}, acquire quite different yet Lorentz-invariant forms in various frames. This somewhat surprising difference can be traced back to a general dependence of the perturbative coefficient functions on lightcone vectors which are introduced by the twist-3 factorization formulae and which are frame-dependent. One can remove this spurious frame dependence by invoking so-called Lorentz invariance relations (LIRs) between twist-3 parton correlation functions. Some of those relations for twist-3 distribution functions were discussed in the literature before. In this paper we derive the corresponding LIRs for twist-3 fragmentation functions. We explicitly demonstrate that these LIRs remove the lightcone vector dependence by considering transverse spin observables in the single-inclusive production of hadrons in lepton-nucleon collisions, $\ell N\to hX$. With the LIRs in hand, we also show that twist-3 observables in general can be written solely in terms of three-parton correlation functions.