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

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

24 pages, LaTeX, 7 eps figures, REVTeX 4

References in corpus (27)

• The Three-Loop Splitting Functions in QCD: The Non-Singlet Case
• The Three-Loop Splitting Functions in QCD: The Singlet Case
• Target Mass Corrections for Polarized Structure Functions and New Sum Rules
• Theory of hard photoproduction
• The Photon Structure from Deep Inelastic Electron-Photon Scattering
• Target mass effects in polarized deep-inelastic scattering
• Virtual Photon Strucutre Functions and the Parton Content of the Electron
• Spin - Dependent Parton Distributions of the Longitudinally Polarized Photon Beyond the Leading Order
• Survey of present data on photon structure functions and resolved photon processes
• Probing the Parton Densities of Virtual Photons at ep Colliders
• Target mass corrections revisited
• Spin-Dependent Structure Functions of Real and Virtual Photons
• Spin-Dependent Structure Functions of the Photon
• Target Mass Effects in QCD Bjorken Sum Rule
• Spin Structure Function of the Virtual Photon Beyond the Leading Order in QCD
• Measurement of the Photon Structure Function at High Q^2 at LEP
• Polarized Parton Distributions in the Photon and Factorization Scheme Dependence
• Has the QCD RG-Improved Parton Content of Virtual Photons been Observed?
• Photon-Parton Splitting Functions at the Next-to-Next-to-Leading Order of QCD
• Factorization Scheme and Parton Distributions in the Polarized Virtual Photon Target
• Electroproduction Cross Section of Large_Et Hadrons at NLO and Virtual Photon Structure Function
• The Virtual Photon Structure to the Next-to-next-to-leading Order in QCD
• Photon 2003: a theorist's summary and outlook
• Polarized Virtual Photon Structure Function $g_2^{\gamma }$ and Twist-3 Effects in QCD
• The $alphaalph{a}_s^2$ corrections to the first moment of the polarized virtual photon structure function $g_1^{g}amma(x,Q^2,P^2)$
• Virtual photon structure functions and positivity constraints
• Longitudinal structure function of the proton at low momentum transfer and extended constituents

Cited by in corpus (6)

• Target mass corrections in lepton--nucleus DIS: theory and applications to nuclear PDFs
• Top quark effects on the virtual photon structure function at ILC
• Heavy quark effects on parton distribution functions in the unpolarized virtual photon up to the next-to-leading order in QCD
• Resummation of large logarithms in the heavy quark effects on the parton distributions inside the virtual photon
• Parton distributions in the virtual photon target up to NNLO in QCD
• NNLO QCD analysis of the virtual photon structure functions