Deep inelastic structure functions of the photon

Three independent structure functions of a real photon can be measured in photon-photon collisions in e^±e^? storage rings. These are M₁ and M_L (related to the usual structure functions W₁andνW₂, as defined for any target) and a third function M₃, which arises from the strong plane polarisation of the colliding photons. We show, using a dispersion relation in the photon mass, that M₃ and the longitudinal structure function M_L both scale and are independent of the vector-dominant hadronic structure of the real photon. Therefore in a parton model, or in the quark light-cone algebra, they are given by the bare quark box diagrams which also dominate when both photons have large q²; this uniquely predicts the behaviour , $\text{M}{}_3\text{= (}\text{1}\text{2}\text{π)Σ e}{}_{\mathrm{i}}{}^4\text{](?x}{}^2\text{)}$ for the real photon structure functions in the Bjorken limit (q₂² → ?∞, q₁²=0, x=?q₂²/2q₁·q₂=constant).