The connection between single transverse spin asymmetries and the second moment of $g_2$

Abstract

We point out that the size of the photon single spin asymmetry in high--energy proton proton collisions with one transversely polarized proton can be related to $d^{(2)}$, the twist three contribution to the second moment of $g_2$. Both quantities should be measured in the near future. The first was analysed by Qiu and Sterman, the second was estimated by Balitsky, Braun, and Kolesnichenko. Both experiments measure effectively the strength of the collective gluon field in the nucleon oriented relative to the nucleon spin. The sum rule results suggest that the single spin asymmetry is rather small for the proton, but could be substantial for the neutron.