Abstract :
The sum rule for the first moment of the polarised (virtual) photon structure function image is revisited in the light of proposals for future image colliders. The sum rule exhibits an array of phenomena characteristic of QCD: for real photons (image) electromagnetic gauge invariance constrains the first moment to vanish; the limit for asymptotic photon virtuality (image) is governed by the electromagnetic image axial anomaly and the approach to asymptopia by the gluonic anomaly; for intermediate values of image, 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 image 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 image 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.
