The polarised photon g1γ sum rule at the linear collider and high luminosity B factories

The sum rule for the first moment of the polarised (virtual) photon structure function g1γ(x,Q2;K2) is revisited in the light of proposals for future e+e− colliders. The sum rule exhibits an array of phenomena characteristic of QCD: for real photons (K2=0) electromagnetic gauge invariance constrains the first moment to vanish; the limit for asymptotic photon virtuality (mρ2≪K2≪Q2) is governed by the electromagnetic UA(1) axial anomaly and the approach to asymptopia by the gluonic anomaly; for intermediate values of K2, it reflects the realisation of chiral symmetry and is determined by the off-shell radiative couplings of the pseudoscalar mesons; finally, like many polarisation phenomena in QCD, the first moment of g1γ involves the gluon topological susceptibility. In this paper, we review the original sum rule proposed by Narison, Shore and Veneziano and extend the relation with pseudoscalar mesons. The possibility of measuring the sum rule in future polarised e+e− colliders is then considered in detail, focusing on the International Linear Collider (ILC) and high luminosity B factories. We conclude that all the above features of the sum rule should be accessible at a polarised collider with the characteristics of SuperKEKB.