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 $x_{\max }(=1/(1+\frac{P^2}{Q^2}))$, the maximal value of $x$, as the ratio $P^2/Q^2$ increases.

• Received 8 January 2008

DOI:https://doi.org/10.1103/PhysRevD.77.054019