The Virtual Photon Structure to the Next-to-next-to-leading Order in QCD

Abstract

We investigate the unpolarized virtual photon structure functions $F_2^{g}amma(x,Q^2,P^2)$ and $F_L^{g}amma(x,Q^2,P^2)$ in perturbative QCD for the kinematical region $Lambd{a}^{2}ll{P}^{2}ll{Q}^2$, where $-Q^2(-P^2)$ is the mass squared of the probe (target) photon and $Lambda$ is the QCD scale parameter. Using the framework of the operator product expansion supplemented by the renormalization group method, we derive the definite predictions for the moments of $F_2^{g}amma(x,Q^2,P^2)$ up to the next-to-next-to-leading order (NNLO) (the order $alphaalph{a}_s$) and for the moments of $F_L^{g}amma(x,Q^2,P^2)$ up to the next-to-leading order (NLO) (the order $alphaalph{a}_s$). The NNLO corrections to the sum rule of $F_2^{g}amma(x,Q^2,P^2)$ are negative and found to be $7$ of the sum of the LO and NLO contributions, when $P^2=1{rmGeV}^2$ and $Q^2=30sim100{rmGeV}^2$ or $P^2=3{rmGeV}^2$ and $Q^2=100{rmGeV}^2$, and the number of active quark flavors $n_f$ is three or four. The NLO corrections to $F_L^{g}amma$ are also negative. The moments are inverted numerically to obtain the predictions for $F_2^{g}amma(x,Q^2,P^2)$ and $F_L^{g}amma(x,Q^2,P^2)$ as functions of $x$.

arXiv comment52 pages, 7 figures; three lines added in section V, two lines added in section VII, references added for section I and V

References in corpus (29)

• Big-Bang nucleosynthesis (Particle Data Group mini-review)
• The Cosmological Parameters 2006
• The Three-Loop Splitting Functions in QCD: The Non-Singlet Case
• The Three-Loop Splitting Functions in QCD: The Singlet Case
• The three-loop QCD $\beta$-function and anomalous dimensions
• Harmonic sums, Mellin transforms and Integrals
• Harmonic Sums and Mellin Transforms up to two-loop Order
• Deep Inelastic Structure Functions at two Loops
• Radiatively Generated Parton Distributions of Real and Virtual Photons
• Theory of hard photoproduction
• The Photon Structure from Deep Inelastic Electron-Photon Scattering
• Analytic Continuation of Mellin Transforms up to two-loop Order
• Analytic Continuation of the Harmonic Sums for the 3--Loop Anomalous Dimensions
• 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
• Two-loop operator matrix elements calculated up to finite terms
• Spin-Dependent Structure Functions of Real and Virtual Photons
• Spin-Dependent Structure Functions of the Photon
• Next-to-next-to-leading order QCD corrections to the photon's parton structure
• Spin Structure Function of the Virtual Photon Beyond the Leading Order in QCD
• 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
• Electroproduction Cross Section of Large_Et Hadrons at NLO and Virtual Photon Structure Function
• Factorization Scheme and Parton Distributions in the Polarized Virtual Photon Target
• Photon 2003: a theorist's summary and outlook
• The $alphaalph{a}_s^2$ corrections to the first moment of the polarized virtual photon structure function $g_1^{g}amma(x,Q^2,P^2)$

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• Heavy quark effects on parton distribution functions in the unpolarized virtual photon up to the next-to-leading order in QCD
• Top quark effects on the virtual photon structure function at ILC
• Resummation of large logarithms in the heavy quark effects on the parton distributions inside the virtual photon
• The real photon structure functions in massive parton model in NLO
• Squark Contributions to Photon Structure Functions and Positivity Constraints
• Parton distributions in the virtual photon target up to NNLO in QCD
• Anomalous GPDs in the photon
• Two-photon physics at future electron-positron colliders
• Virtual Photon Structure Functions to NNLO in QCD