Virtual photon structure functions and positivity constraints

Abstract

We study the three positivity constraints among the eight virtual photon structure functions, derived from the Cauchy-Schwarz inequality and which are hence model-independent. The photon structure functions obtained from the simple parton model show quite different behaviors in a massive quark or a massless quark case, but they satisfy, in both cases, the three positivity constraints. We then discuss an inequality which holds among the unpolarized and polarized photon structure functions $F_1^{\gamma }$, $g_1^{\gamma }$ and $W_{TT}^{\tau }$, in the kinematic region ${\Lambda }^2\ll P^2\ll Q^2$, where $-Q^2(-P^2)$ is the mass squared of the probe (target) photon, and we examine whether this inequality is satisfied by the perturbative QCD results.

Comments: 24 pages, 13 eps figures