hep-ph/0311313

From: Claudio Coriano [view email]
Date (v1): Tue, 25 Nov 2003 09:45:20 GMT   (100kb)
Date (revised v2): Thu, 15 Apr 2004 18:16:29 GMT   (100kb)

Direct Solution of Renormalization Group Equations of QCD in $x-$space: NLO Implementations at Leading Twist
Authors: Alessandro Cafarella, Claudio Coriano'
Comments: 31 pages, 15 figs, replaced with revised final version, to be published by Comp. Phys. Comm
Journal-ref: Comput.Phys.Commun. 160 (2004) 213-242

    We illustrate the implementation of a method based on the use of recursion relations in (Bjorken) $x-$space for the solution of the evolution equations of QCD for all the leading twist distributions. The algorithm has the advantage of being very fast. The implementation that we release is written in C and is performed to next-to-leading order in $\alpha_s$. 


e-Print: hep-ph/0512358
 Nnlo logarithmic expansions and exact solutions of the DGLAP equations from x-space: New algorithms for precision studies at the lhc.
Alessandro Cafarella (Crete U.) , Claudio Coriano' (Lecce U. & INFN, Lecce & Liverpool U., Dept. Math.) , Marco Guzzi (Liverpool U., Dept. Math.) . LTH-679, Dec 2005. 56pp.
Published in Nucl.Phys.B748:253-308,2006.


hep-ph/0510295 [abs, ps, pdf, other] :
    Title: DGLAP evolution of truncated moments of parton densities within two different approaches
    Authors: D. Kotlorz, A. Kotlorz
    Comments: 17 pages, 6 figures
    Journal-ref: Acta Phys. Pol. B 36, 3023 (2005)

    We solve the LO DGLAP QCD evolution equation for truncated Mellin moments of the nucleon nonsinglet structure function. The results are compared with those, obtained in the Chebyshev-polynomial approach for $x$-space solutions. Computations are performed for a wide range of the truncation point $10^{-5}\leq x_0\leq 0.9$ and $1\leq Q^2\leq 100 {\rm GeV}^2$. The agreement is perfect for higher moments ($n\geq 2$) and not too large $x_0$ ($x_0\leq 0.1$), even for a small number of terms in the truncated series (M=4). The accuracy of the truncated moments method increases for larger $M$ and decreases very slowly with increasing $Q^2$. For M=30 the relative error in a case of the first moment at $x_0\leq 0.1$ and $Q^2=10 {\rm GeV}^2$ doesn't exceed 5% independently on the shape of the input parametrisation. This is a quite satisfactory result. Using the truncated moments approach one can avoid uncertainties from the unmeasurable $x\to 0$ region and also study scaling violations without making any assumption on the shape of input parametrisation of parton distributions. Therefore the method of truncated moments seems to be a useful tool in further QCD analyses. 



hep-ph/0604248 [abs, ps, pdf, other] :
    Title: Code for prompt numerical computation of the leading order GPD evolution
    Authors: A.V. Vinnikov
    Comments: 14 pages, 8 figures, source code at this http URL

    This paper describes the design and work of a set of computer routines capable for numerical computation of generalized parton distributions (GPDs) evolution at the leading order. The main intention of this work is to present a fast-working computer code making possible fitting of GPDs parameters to the data on hard electron-nucleon scattering.
     


 hep-ph/0605040 [abs, pdf] :
    Title: Taylor expansion method to solve Dokshitzer-Gribov-Lipatov- Altarelli-Parisi equations in leading and next-to-leading orders at small-x
    Authors: R Rajkhowa, J K Sarma
    Comments: 37 pages, 19 figures

    We present particular and unique solutions of singlet and non-singlet Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations in leading order (LO) and next-to-leading order (NLO) and gluon, sea and valence quark Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations in leading order (LO) by applying Taylor expansion method at small-x. We obtain t-evolutions of deuteron, proton, neutron, difference and ratio of proton and neutron, gluon, light sea and valence quark structure functions and x-evolution of deuteron,gluon and light sea quark structure functions at small-x from DGLAP evolution equations. The results of tevolutions are compared with HERA and NMC low-x low-Q2 data and x-evolutions are compared with NMC low-x low-Q2 data and recent global parameterization. And also we compare our results of t-evolution of proton structure functions with a recent global parameterization. 


 arXiv:0704.3344 [ps, pdf, other] :
    Title: Solving the QCD NLO evolution equations with a Markovian Monte Carlo
    Authors: W. Placzek, K. Golec-Biernat, S. Jadach, M. Skrzypek
    Comments: 12 pages, 2 eps figures

    We discuss precision Monte Carlo (MC) calculations for solving the QCD evolution equations up to the next-to-leading-order (NLO) level. They employ forward Markovian Monte Carlo algorithms, which provide rigorous solutions of the above equations. These algorithms are implemented in the form of the Monte Carlo program EvolFMC. This program has been cross-checked with independent, non-MC, programs (QCDNum16 and APCheb33) and the numerical agreement at the level of 0.1% has been found.