Virtual Photon Structure Functions and Positivity Constraints

We study the three positivity constraints among the eight structure functions of virtual photon, derived from the Cauchy-Schwarz inequality and hence, which are model independent. The photon structure functions obtained from the simple parton model show quite different behaviors either in a massive quark case or in a massless one, 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 γ 1 , g γ 1 and W τ TT , in the kinematical region Λ 2 ≪ P 2 ≪ Q, where −Q2(−P ) is the mass squared of the probe (target) photon, and we test the positivity constraint for the perturbative QCD results on these functions. YNU-HEPTh-02-102 CPT-2002/PE.4346 KUCP-207 May 2002 e-mail address: [email protected] e-mail address: [email protected] e-mail address: [email protected]