Transition from real to virtual polarized photon structures

Abstract

We investigate the transition of the polarized photon structure function $g_1^\gamma(x,Q^2,P^2)$ when the target photon shifts from on-shell ($P^2=0$) to far off-shell ($P^2\gg \Lambda^2$) region. The analysis is performed to the next-to-leading order in QCD. The first moment of $g_1^\gamma$ which vanishes for the real photon, turns to be a negative value when target photon becomes off-shell. The explicit $P^2$-dependence of the first moment sum rule as well as of the structure function $g_1^\gamma(x,Q^2,P^2)$ as a function of $x$ is studied in the framework of the vector meson dominance model.