We present an implementation of the Linked Dipole Chain model for deeply inelastic ep scattering into the framework of the Ariadne event generator. Using this implementation we obtain results both for the inclusive structure function as well as for exclusive properties of the hadronic final state. * The original publication was based on results from an implementation containing an error. In this revised version this error has been corrected, some of the beyond leading-log assumptions have been revised and so have some of the results.
We present approximations of varying degree of sophistication to the integral equations for the ͑gluon͒ structure functions of a hadron ͑''the partonic flux factor''͒ in a model valid in the leading log approximation with a running coupling constant. The results are all of the BFKL type, i.e., a power in the Bjorken variable x B Ϫ with the parameter determined from the size ␣ 0 of the ''effective'' running coupling ␣ ϵ3␣ s / ϭ␣ 0 /ln(k Ќ 2 ) and varying depending upon the treatment of the transverse momentum pole. We also consider the implications for the transverse momentum (k Ќ ) fluctuations along the emission chains and we obtain an exponential falloff in the relevant ϵln(k Ќ 2 ) variable, i.e., an inverse power (k Ќ 2 ) Ϫ(2ϩ) with the same parameter . This is different from the BFKL result for a fixed coupling, where the distributions are Gaussian in the variable with a width as in a Brownian motion determined by ''the length'' of the emission chains, i.e., ln(1/x B ). The results are verified by a realistic Monte Carlo simulation and we provide a simple physics motivation for the change. ͓S0556-2821͑98͒00811-X͔ PACS number͑s͒: 12.38.Bx, 12.38.Aw
Abstract:A computer program for evaluating colour factors of QCD Feynman diagrams is presented, and illustrative examples on how to use the program to calculate non trivial colour factors are given. The program and the discussion in this paper is based on a diagrammatic approach to colour factors. Method of solution: QCD Feynman diagrams, with no four-gluon vertices, factorize into a colour (group) factor and a kinematical factor. The colour part of any closed QCD Feynman diagram can be transformed into a sum of diagrams including only closed quark (colour) lines. In each such term, the number of quark (colour) loops is counted, giving factors of 3 (or N c ). The sum of these terms is then the desired colour factor. To perform the translation, we need to have rules to interpret gluons and vertices into quark lines. There is in principle only need for three equalities to be able to calculate any closed QCD diagram (not containing four gluon vertices). To achieve good computing performance further equalities have been introduced. The most essential ones are listed in Appendix A.Restriction of complexity of the problem: Four gluon vertices cannot be included directly in diagrams to be calculated. The number of gluons in diagrams to be calculated are limited to 200, but can easily be changed prior to compiling.
Typical running time:For typical diagrams, fractions of a second. Complicated diagramsa few seconds to hours.
We present several implementations of the Metropolis method, an adaptive
Monte Carlo algorithm, which allow for the calculation of multi-dimensional
integrals over arbitrary on-shell four-momentum phase space. The Metropolis
technique reveals itself very suitable for the treatment of high energy
processes in particle physics, particularly when the number of final state
objects and of kinematic constraints on the latter gets larger. We compare the
performances of the Metropolis algorithm with those of other programs widely
used in numerical simulations.Comment: 28+3 pages, To appear in Computer Physics Communications. One proof
revised, to appear as Erratum in CP
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