Low- and high-mass components of the photon distribution functions

The structure of the general solution of the inhomogeneous evolution equations allows the separation of a photon structure function into perturbative (``anomalous") and non-perturbative contributions. The former part is fully calculable, and can be identified with the high-mass contributions to the dispersion integral in the photon mass. Properly normalized ``state" distributions can be defined, where the \gamma\to\qqbar splitting probability is factored out. These state distributions are shown to be useful in the description of the hadronic event properties, and necessary for a proper eikonalization of jet cross sections. Convenient parametrizations are provided both for the state and for the full anomalous parton distributions. The non-perturbative parts of the parton distribution functions of the photon are identified with the low-mass contributions to the dispersion integral. Their normalizations, as well as the value of the scale $Q_0$ at which the perturbative parts vanish, are fixed by approximating the low-mass contributions by a discrete, finite sum of vector mesons. The shapes of these hadronic distributions are fitted to the available data on $F_2^\gamma(x,Q^2)$. Parametrizations are provided for $Q_0=0.6\,$GeV and $Q_0=2\,$GeV, both in the DIS and the $\overline{\mathrm{MS}}$ factorization schemes. The full parametrizations are extended towards virtual photons. Finally, the often-used ``FKP-plus-TPC/$2\gamma$" solution for $F_2^\gamma(x,Q^2)$ is commented upon.Comment: 33 pages, Latex, 6 Z-compressed and uuencoded figure

New Parton Distribution Functions for the Photon

We present new improved parton distributions for the photon. We fit {\bf all} available data on the photon structure function, $F^{\gamma}_{2}(x,Q^2)$, with $Q^2\ge 3$ GeV$^2$, in order to determine the quark distributions. We also pay particular attention to the gluon distribution in the photon, $g^{\gamma}(x,Q^2)$, which has been poorly constrained in earlier analyses which only include structure function data. We use large $p_T$ jet production in $\gamma \gamma$ collisions from TRISTAN to constrain $g^\gamma$. We also see what information can be gleaned from $\gamma p$ collisions at HERA on $g^{\gamma}$ and on the quark distributions at large $x$, where there are no structure function data. We review future prospects of elucidating the parton distributions of the photon.Comment: 33 pages, 8 figures, uses eps

D* Production in Deep Inelastic Scattering at HERA

This paper presents measurements of D^{*\pm} production in deep inelastic scattering from collisions between 27.5 GeV positrons and 820 GeV protons. The data have been taken with the ZEUS detector at HERA. The decay channel $D^{*+}\to (D^0 \to K^- \pi^+) \pi^+$ (+ c.c.) has been used in the study. The $e^+p$ cross section for inclusive D^{*\pm} production with $5<Q^2<100 GeV^2$ and $y<0.7$ is 5.3 \pms 1.0 \pms 0.8 nb in the kinematic region {$1.3<p_T(D^{*\pm})<9.0$ GeV and $| \eta(D^{*\pm}) |<1.5$}. Differential cross sections as functions of p_T(D^{*\pm}), $\eta(D^{*\pm}), W$ and $Q^2$ are compared with next-to-leading order QCD calculations based on the photon-gluon fusion production mechanism. After an extrapolation of the cross section to the full kinematic region in p_T(D^{*\pm}) and $\eta$(D^{*\pm}), the charm contribution $F_2^{c\bar{c}}(x,Q^2)$ to the proton structure function is determined for Bjorken $x$ between 2 $\cdot$ 10$^{-4}$ and 5 $\cdot$ 10$^{-3}$.Comment: 17 pages including 4 figure

Symbolic State-Space Exploration and Guard Generation in Supervisory Control Theory

Supervisory Control Theory (SCT) is a model-based framework for automatically synthesizing a supervisor that minimally restricts the behavior of a plant such that given specifications is fulfilled. The main obstacle which prevents SCT from having a major industrial breakthrough is that the supervisory synthesis, consisting of a series of reachability tasks, suffers from the state-space explosion problem. To alleviate this problem, a well-known strategy is to represent and explore the state-space symbolically by using Binary Decision Diagrams. Based on this principle, an alternative symbolic state-space traversal approach, depending on the disjunctive partitioning technique, is presented in this paper. In addition, the approach is adapted to the prior work, the guard generation procedure, to extract compact propositional formulae from a symbolically represented supervisor. These propositional formulae, referred to as guards, are then attached to the original model, resulting in a modular and comprehensible representation of the supervisor