The Connection between Single Transverse Spin Asymmetries and the Second Moment of G 2

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. Recent polarized deep inelastic lepton nucleon scattering experiments [1, 2, 3] have generated great interest in the spin structure of the nucleons. It seems that polarized reactions will develop into an ideal testing ground for QCD. So far only longitudinal polarization was studied, but transverse polarization could offer a wealth of novel effects and will be studied in detail by future experiments. In deep inelastic scattering the interest is focused on the polarized distribution function g 2 (x) which was already extensively analysed theoretically [4, 5, 6, 7]. In these investigations unsuppressed twist three contributions d (n) to the n-th moment of g 2 (x) are most interesting. d (2) should be measurable with good statistics e.g. by the HERMES [8] experiment. In priciple a plethora of transverse spin effects should be observable in polarized proton-proton collisions. However, the expected asymmetries in these reactions are usually very small, typically of the order of 1 % or less. Furthermore it will still take a number of years before polarized proton-proton collisions become feasible at any accelerator, the ideal place definitely being RHIC. What is possible in the near future are single spin experiments with a polarized target and an unpolarized beam and these are under intensive consideration.