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

We investigate 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. Using the framework of the operator product expansion supplemented by the renormalization group method, we derive the definite predictions for the moments of $F_2^gamma(x,Q^2,P^2)$ up to the next-to-next-to-leading order (NNLO) (the order $alphaalpha_s$) and for the moments of $F_L^gamma(x,Q^2,P^2)$ up to the next-to-leading order (NLO) (the order $alphaalpha_s$). The NNLO corrections to the sum rule of $F_2^gamma(x,Q^2,P^2)$ are negative and found to be $7$ of the sum of the LO and NLO contributions, when $P^2=1 {rm GeV}^2$ and $Q^2=30sim 100 {rm GeV}^2$ or $P^2=3 {rm GeV}^2$ and $Q^2=100 {rm GeV}^2$, and the number of active quark flavors $n_f$ is three or four. The NLO corrections to $F_L^gamma$ are also negative. The moments are inverted numerically to obtain the predictions for $F_2^gamma(x,Q^2,P^2)$ and $F_L^gamma(x,Q^2,P^2)$ as functions of $x$

Virtual Photon Structure Functions

We discuss the perturbatively calculable virtual photon structure functions. First we present the framework for analyzing the structure functions of the virtual photon and derive a first moment of $g_1^\gamma$ of the virtual photon. We then investigate the three positivity constraints satisfied by the eight structure functions of the virtual photon.Comment: 5 pages, LaTeX, 5 eps figures, npb.sty file included Talk given at RADCOR/Loops and Legs 2002, Kloster Banz, Germany, September 8-13, 2002, to appear in the Proceeding

Policy Decision by Election

本稿は経済政策の3つの異質な原理の意義と限界とを指摘し（第I節），それを克服する方法としてダウンズの理論を紹介し（第II節），かつ主としてシェップルに依拠しながら，ダウンズ理論の定式化を試みた（第III節）ものである