Virtual Photon Structure Functions to NNLO in QCD

TL;DR

This paper calculates the virtual photon structure functions in perturbative QCD up to NNLO, providing precise theoretical predictions for their moments in a specific kinematic regime.

Contribution

It presents the first NNLO (next-to-next-to-leading order) calculations of the virtual photon structure functions' moments in QCD, extending previous NLO results.

Findings

Derived NNLO predictions for $F_2^ ext{gamma}$ moments.

Provided NLO predictions for $F_L^ ext{gamma}$ moments.

Clarified the behavior of structure functions in the $ ext{QCD}$ perturbative regime.

Abstract

The unpolarized virtual photon structure functions $F_2^\gamma(x,Q^2,P^2)$ and $F_L^\gamma(x,Q^2,P^2)$ are investigated in perturbative QCD for the kinematical region $\Lambda^2 \ll P^2 \ll Q^2$, where $-Q^2(-P^2)$ is the mass squared of the probe (target) photon and $\Lambda$ is the QCD scale parameter. In the framework of operator product expansion supplemented by the renormalization group method, the definite predictions are derived for the moments of $F_2^\gamma(x,Q^2,P^2)$ up to the next-to-next-to-leading order (the order $\alpha\alpha_s$) and for the moments of $F_L^\gamma(x,Q^2,P^2)$ up to the next-to-leading order (the order $\alpha\alpha_s$)