Determining the Spin Structure of the Photon at Future Colliders

Nothing is known experimentally about the parton content of circularly polarized photons, defined by ∆f(x,Q) ≡ f + (x,Q2)− f γ+ − (x,Q), where f γ+ + (f γ+ − ) denotes the density of a parton f with helicity ‘+’ (‘−’) in a photon with helicity ‘+’, and the next round of spin experiments, Compass and Rhic, is not sensitive to these distributions either. The ∆f contain information different from that contained in the unpolarized ones, f , and their measurement is vital for a complete understanding of the partonic structure of photons. It has been demonstrated 1 that measurements of the structure function g 1 and of di-jet spin asymmetries at a future polarized linear ee collider can provide valuable information about ∆f . Di-jet spin asymmetries at Hera running in a polarized collider mode, appear to be equally promising . Here we will focus on two other recent proposals for a polarized ep collider: eRhic and THera. As in 1,2,3 we will exploit the predictions of two very different models for the ∆f , and study the sensitivity of di-jet production to these unknown quantities. In the first case (‘maximal scenario’) we saturate the positivity bound |∆fγ(x,Q2)| ≤ f(x,Q) at a low input scale μ ≃ 0.6GeV, using the unpolarized GRV densities f . The other extreme input (‘minimal scenario’) is defined by a vanishing hadronic input at the scale μ. We limit ourselves to leading order (LO) QCD, which is entirely sufficient for our purposes; however both scenarios can be straightforwardly extended to next-to-leading order .