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

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 ${\Lambda }^2\ll P^2\ll Q^2$, 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 $\overline{\mathrm{MS}}$ and ${\mathrm{DIS}}_{\gamma }$ schemes, and discuss their scheme dependence. We show that the factorisation-scheme dependence is characterised by the large-$x$ behaviours of quark distributions. Gluon distribution is predicted to be very small in absolute value except in the small-$x$ region.

Comments: 28 pages, 5 figures, version to appear in Eur. Phys. J. C