Squark contributions to photon structure functions and positivity constraints

Abstract

Photon structure functions in supersymmetric QCD are investigated in terms of the parton model where squark contributions are evaluated. We calculate the eight virtual photon structure functions by taking the discontinuity of the squark massive one-loop diagrams of the photon-photon forward amplitude. The model-independent positivity constraints derived from the Cauchy-Schwarz inequalities are satisfied by the squark parton model calculation and actually the two equality relations hold for the squark contribution. We also show that our polarized photon structure function ${g}_{1}^{\ensuremath{\gamma}}$ for the real photon leads to the vanishing first moment sum rule, and the constraint $|{g}_{1}^{\ensuremath{\gamma}}|\ensuremath{\le}{F}_{1}^{\ensuremath{\gamma}}$ is satisfied by the real photon. We also discuss a squark signature in the structure function ${W}_{TT}^{\ensuremath{\tau}}$.