Target Mass Corrections for the Virtual Photon Structure Functions to the Next-to-next-to-leading Order in QCD

TL;DR

This paper calculates target mass corrections to the unpolarized virtual photon structure functions in perturbative QCD up to NNLO for a specific kinematic region, revealing significant effects at large x values.

Contribution

It provides the first closed-form expressions for target mass corrected structure functions up to NNLO, extending previous analyses to higher precision.

Findings

Target mass effects are significant at large x and near the maximum x value.

The derived formulas include corrections up to NNLO for F2 and NLO for FL.

Numerical analysis shows the importance of these corrections in certain kinematic regimes.

Abstract

We investigate target mass effects in the unpolarized virtual photon structure functions $F_2^\gamma(x,Q^2,P^2)$ and $F_L^\gamma(x,Q^2,P^2)$ 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. We obtain the Nachtmann moments for the structure functions and then, by inverting the moments, we get the expressions in closed form for $F_2^\gamma(x,Q^2,P^2)$ up to the next-to-next-to-leading order and for $F_L^\gamma(x,Q^2,P^2)$ up to the next-to-leading order, both of which include the target mass corrections. Numerical analysis exhibits that target mass effects appear at large $x$ and become sizable near $x_{\rm max}(=1/(1+\frac{P^2}{Q^2}))$, the maximal value of $x$, as the ratio $P^2/Q^2$ increases.