Eur. Phys. J. C (2009) 62: 467-480
https://doi.org/10.1140/epjc/s10052-009-1062-7

Regular Article - Theoretical Physics

Parton distributions in the virtual photon target up to NNLO in QCD

¹ Graduate School of Pure and Applied Sciences, University of Tsukuba, Tsukuba, Ibaraki, 305-8571, Japan
² Dept. of Physics, Faculty of Engineering, Yokohama National University, Yokohama, 240-8501, Japan
³ Dept. of Physics, Graduate School of Science, Kyoto University, Yoshida, Kyoto, 606-8501, Japan

^* e-mail: sasaki@phys.ynu.ac.jp

Received: 17 February 2009
Revised: 15 April 2009
Published online: 3 June 2009

Abstract

Parton distributions in the virtual photon target are investigated in perturbative QCD up to the next-to-next-to-leading order (NNLO). In the case Λ ²≪P ²≪Q ², where −Q ² (−P ²) is the mass squared of the probe (target) photon, parton distributions can be predicted completely up to the NNLO, but they are factorisation-scheme dependent. We analyse parton distributions in two different factorisation schemes, namely the and DIS _γ schemes, and we discuss their scheme dependence. We show that the factorisation-scheme dependence is characterised by the large-x behaviours of the quark distributions. The gluon distribution is predicted to be very small in absolute value except in the small-x region.