The $alpha alpha_s^2$ corrections to the first moment of the polarized virtual photon structure function $g_1^gamma(x,Q^2,P^2)$

K. Sasaki; T. Ueda; T. Uematsu

doi:10.1103/PhysRevD.73.094024

paper

The $a l p haa l p h a_{s}^{2}$ corrections to the first moment of the polarized virtual photon structure function $g_{1}^{g} amma (x, Q^{2}, P^{2})$

arXiv:hep-ph/0604130 · doi:10.1103/PhysRevD.73.094024

Abstract

We present the next-to-next-to-leading order ( $a l p haa l p h a_{s}^{2}$ ) 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 $L amb d a^{2} l l P^{2} l l Q^{2}$ , where $- Q^{2} (- P^{2})$ is the mass squared of the probe (target) photon and $L amb d a$ 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 $a l p haa l p h a_{s}^{2}$ corrections are found to be about 3% of the sum of the leading order ( $a l p ha$ ) andthe next-to-leading order ( $a l p haa l p h a_{s}$ ) contributions, when $Q^{2} = 30 s im 100 r m G e V^{2}$ and $P^{2} = 3 r m G e V^{2}$ , and the number of active quark flavors $n_{f}$ is three to five.

21 pages

The alphaalphas2​ corrections to the first moment of the polarized virtual photon structure function g1g​amma(x,Q2,P2)

Abstract

The $a l p haa l p h a_{s}^{2}$ corrections to the first moment of the polarized virtual photon structure function $g_{1}^{g} amma (x, Q^{2}, P^{2})$