Gluon polarization in nucleons

Abstract

In QCD the gauge-invariant gluon polarization $\Delta G$ in a nucleon can be defined either in a non-local way as the integral over the Ioffe-time distribution of polarized gluons, or in light-cone gauge as the forward matrix element of the local topological current. We have investigated both possibilities within the framework of QCD sum rules. Although the topological current is built from local fields, we have found that its matrix element retains sensitivity to large longitudinal distances. Because QCD sum rules produce artificial oscillations of the Ioffe-time distribution of polarized glue at moderate and large light-like distances, the calculation of the matrix element of the topological current results in a small value of $\Delta G(\mu^2 \sim 1\,{\rm GeV}^2) \approx 0.6 \pm 0.2$ . In a more consistent approach QCD sum rules are used to describe the polarized gluon distribution only at small light-like distances. Assuming that significant contributions to $\Delta G$ arise only from longitudinal length scales not larger than the nucleon size leads to $\Delta G(\mu^2 \sim 1\,{\rm GeV}^2) \approx 2 \pm 1$ .