Operator constraints for twist-3 functions and Lorentz invariance properties of twist-3 observables

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, 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 leptonnucleon collisions, N → 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.

Cross section and transverse single-spin asymmetry ofηmesons inp↑+pcollisions atAdare1, Aidala2, Ajitanand3 et al. 2014Phys. Rev. D353110View full textAdd to dashboardCite

“…While these correlation functions do not contain direct information on the transverse momentum distributions of partons, this approach has been related to k T -moments of TMD PDFs and FFs such as the Sivers and Collins functions for multiparton correlations in the initial and final state, respectively [38]. Prior RHIC transverse SSA measurements for inclusive hadron production have been described relatively well by a combination of twist-3 effects in the initial and final states [39][40][41][42], but further refinement in both the theoretical calculations, for example through a better understanding of uncertainties, and in experimental measurements, for example through multi-differential measurements in more than one kinematic variable simultaneously, will be needed to test and understand these correlations in detail.…”

Connections between TMDs and collinear twist-3 functions within the context of single-spin asymmetries

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New approach to the Sivers effect in the collinear twist-3 formalism

“…By using the translation invariance [15], 1T (x) has another definition using the quark TMD correlator. Here we recall the definition of the quark Sivers function [34],…”