The $alphaalph{a}_s^2$ corrections to the first moment of the polarized virtual photon structure function $g_1^{g}amma(x,Q^2,P^2)$

Abstract

We present the next-to-next-to-leading order ($alphaalph{a}_s^2$) corrections to the first moment of the polarized virtual photon structure function $g_1^{g}amma(x,Q^2,P^2)$ in the kinematical region $Lambd{a}^{2}ll{P}^{2}ll{Q}^2$, where $-Q^2(-P^2)$ is the mass squared of the probe (target) photon and $Lambda$ is the QCD scale parameter. In order to evaluate the three-loop-level photon matrix element of the flavor singlet axial current, we resort to the Adler-Bardeen theorem for the axial anomaly and we calculate in effect the two-loop diagrams for the photon matrix element of the gluon operator. The $alphaalph{a}_s^2$ corrections are found to be about 3% of the sum of the leading order ($alpha$) andthe next-to-leading order ($alphaalph{a}_s$) contributions, when $Q^2=30sim100{rmGeV}^2$and $P^2=3{rmGeV}^2$, and the number of active quark flavors $n_f$ is three to five.

Comments: 21 pages