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

TL;DR

This paper calculates parton distributions in the virtual photon up to NNLO in QCD, analyzing scheme dependence and behavior at different momentum fractions, providing precise predictions for high-energy photon interactions.

Contribution

It provides the first NNLO predictions for parton distributions in the virtual photon and examines their scheme dependence in detail.

Findings

Parton distributions can be predicted up to NNLO in the specified kinematic region.

Scheme dependence is significant at large x due to quark distribution behavior.

Gluon distribution remains very small except at small x.

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 $\bar{\rm MS}$ and ${\rm DIS}_{\gamma}$ 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.