Novel relations for twist-3 tensor-polarized fragmentation functions in spin-1 hadrons

TL;DR

This paper derives theoretical relations among twist-3 fragmentation functions for tensor-polarized spin-1 hadrons, ensuring frame independence and connecting them to twist-2 functions, aiding future experimental analysis.

Contribution

It introduces Lorentz-invariance and QCD equation of motion relations for twist-3 FFs of spin-1 hadrons, and decomposes them into twist-2 and three-parton FFs, including Wandzura-Wilczek type relations.

Findings

Derived Lorentz-invariance relations for twist-3 FFs.

Presented QCD equation of motion relations for tensor-polarized FFs.

Expressed twist-3 FFs in terms of twist-2 FFs when neglecting dynamical contributions.

Abstract

There are three types of fragmentation functions (FFs) which are used to describe the twist-3 cross sections of the hard semi-inclusive processes under QCD collinear factorization, and they are called intrinsic, kinematical, and dynamical FFs. In this work, we investigate the theoretical relations among these FFs for a tensor-polarized spin-1 hadron. Three Lorentz-invariance relations are derived by using the identities between the nonlocal quark-quark and quark-gluon-quark operators, which guarantee the frame independence of the twist-3 spin observables. The QCD equation of motion relations are also presented for the tensor-polarized FFs. In addition, we show that the intrinsic and kinematical twist-3 FFs can be decomposed into the contributions of twist-2 FFs and twist-3 three-parton FFs, and the latter are also called dynamical FFs. If one neglects the dynamical FFs, we can obtain relations which are analogous to the Wandzura-Wilczek relation. Then, the intrinsic and kinematical twist-3 FFs are expressed in terms of the leading-twist ones. Since the FFs of a spin-1 hadron can be measured at various experimental facilities in the near future, these theoretical relations will play an important role in the analysis of the collinear tensor-polarized FFs.