Transverse-spin gluon distribution function

TL;DR

This paper introduces a new transverse-spin gluon distribution function in QCD, providing a unified operator framework and exploring its implications for nucleon spin structure.

Contribution

It defines the transverse-spin gluon distribution function $G_T(x)$ using a spin-operator approach, extending the classification of collinear parton distributions to twist three.

Findings

$G_T(x)$ is expressed as a sum of chromoelectric and chromomagnetic correlators.

$G_T(x)$ includes three-gluon and quark-gluon correlation effects.

The first moment of $G_T(x)$ relates to the transverse nucleon spin decomposition.

Abstract

We introduce the spin-operator representation for the gluon as well as quark distribution functions as nucleon matrix element of the gauge-invariant bilocal light-cone operators in QCD. To identify the relevant spin operators for quarks and gluons in a unified manner, we rely on the transformation properties of the quark and gluon fields in the coordinate space under the action of the generator of the Lorentz group. In particular, this approach allows us to define the transverse-spin gluon distribution function $G_T(x)$, which is the genuine counterpart of the transverse-spin quark distribution function $g_T(x)$ relevant to the transverse-spin structure function $g_2(x, Q^2)$ in the deep inelastic scattering. We show that $G_T(x)$ is given by the sum of the chromoelectric and chromomagnetic correlators associated with helicity-flip by one unit, and the treatment of the latter correlator completes the classification of the collinear parton distribution functions up to twist three. We show that $G_T(x)$ receives the three-gluon and quark-gluon correlation effects and discuss the operator product expansion for $G_T(x)$. We also discuss the relevance of the first moment of $G_T(x)$ for the partonic decomposition of the transverse nucleon spin.