Spin Structure Function of the Virtual Photon Beyond the Leading Order in QCD

Abstract

Polarized photon structure can be studied in the future polarized $e^{+}{e}^{-}$ colliding-beam experiments. We investigate the spin-dependent structure function of the virtual photon $g_1^{\gamma }(x,Q^2,P^2)$, in perturbative QCD for ${\Lambda }^2\ll P^2\ll Q^2$, where $-Q^2$ ($-P^2$) is the mass squared of the probe (target) photon. The analysis is performed to next-to-leading order in QCD. We particularly emphasize the renormalization scheme independence of the result.The non-leading corrections significantly modify the leading log result, in particular, at large $x$ as well as at small $x$. We also discuss the non-vanishing first moment sum rule of $g_1^{\gamma }$, where $\mathcal{O}({\alpha }_s)$ corrections are computed.

Comments: 39 pages, LaTeX, 6 Postscript Figures, eqsection.sty file included