Constrained non-Markovian Monte Carlo modelling of the evolution equation in QCD

A new class of the constrained Monte Carlo (CMC) algorithms for the QCD evolution equation was recently discovered. The constraint is imposed on the type and the total longitudinal energy of the parton exiting QCD evolution and entering a hard process. The efficiency of the new CMCs is found to be r...

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Detalles Bibliográficos
Autores principales: Jadach, S., Skrzypek, M.
Lenguaje:eng
Publicado: CERN 2005
Materias:
Particle Physics - Phenomenology
Acceso en línea:http://cds.cern.ch/record/885053
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author Jadach, S.
Skrzypek, M.
author_facet Jadach, S.
Skrzypek, M.
author_sort Jadach, S.
collection CERN
description A new class of the constrained Monte Carlo (CMC) algorithms for the QCD evolution equation was recently discovered. The constraint is imposed on the type and the total longitudinal energy of the parton exiting QCD evolution and entering a hard process. The efficiency of the new CMCs is found to be reasonable.
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institution Organización Europea para la Investigación Nuclear
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spelling cern-8850532023-03-14T17:15:30Zhttp://cds.cern.ch/record/885053engJadach, S.Skrzypek, M.Constrained non-Markovian Monte Carlo modelling of the evolution equation in QCDParticle Physics - PhenomenologyA new class of the constrained Monte Carlo (CMC) algorithms for the QCD evolution equation was recently discovered. The constraint is imposed on the type and the total longitudinal energy of the parton exiting QCD evolution and entering a hard process. The efficiency of the new CMCs is found to be reasonable.A new class of the constrained Monte Carlo (CMC) algorithms for the QCD evolution equation was recently discovered. The constraint is imposed on the type and the total longitudinal energy of the parton exiting QCD evolution and entering a hard process. The efficiency of the new CMCs is found to be reasonable.A new class of the constrained Monte Carlo (CMC) algorithms for the QCD evolution equation was recently discovered. The constraint is imposed on the type and the total longitudinal energy of the parton exiting QCD evolution and entering a hard process. The efficiency of the new CMCs is found to be reasonable.A new class of the constrained Monte Carlo (CMC) algorithms for the QCD evolution equation was recently discovered. The constraint is imposed on the type and the total longitudinal energy of the parton exiting QCD evolution and entering a hard process. The efficiency of the new CMCs is found to be reasonable.A new class of the constrained Monte Carlo (CMC) algorithms for the QCDevolution equation was recently discovered. The constraint is imposed on thetype and the total longitudinal energy of the parton exiting QCD evolution andentering a hard process. The efficiency of the new CMCs is found to bereasonable. This brief report summarizes the recent developments in the area ofthe Monte Carlo (MC) techniques for the perturbative QCD calculations. Most ofit was done at the time of the present HERA–LHC workshop, partial results beingpresented at several of its meetings. At present, two papers, [1] and [2],demonstrating the principal results are already available. Generally, these MCtechniques concern the QCD evolution of the parton distribution functions (PDFs)D k (x, Q), where k denotes the type of the parton (quark, gluon), x thefraction of longitudinal momentum of the initial hadron carried by the par-ton,and the size of the available real/virtual emission phase space is Q. Theevolution equation describes the response of the PDF to an increase of Q; D k(x, Q) is an inclusive distribution and can be measured almost directly inhadron — lepton scattering. On the other hand, it was always known that thereexists in QCD an exclusive picture of the PDF, the so-called parton-showerprocess, in which D k (x, Q) is the distribution of the parton exiting theemission chain and entering the hard process (lepton–quark for example). Thekernel functions P kj (Q, z), that govern the differential evolution equationsof PDFs are closely related to distributions governing a single emission process(i − 1) → i in the parton shower: P k i k i−1 (Q i , x i /x i−1). In otherwords, the evolution (Q-dependence) of PDFs and the parton shower represent twofaces of the same QCD reality. The first one (inclusive) is well suited forbasic precision tests of QCD at hadron–lepton colliders, while the second one(exclusive) provides realistic exclusive Monte Carlo mod-eling, vitally neededfor experiments at high-energy particle colliders. At this point, it is worthstressing that, so far, we were referring to DGLAP-type PDFs [3] and theirevolution, and to constructing a parton-shower MC starting from them, as wasdone two decades ago and is still done today. This involves a certain amount of" backward engineering " and educated guesses, because the classical inclusivePDFs integrate over the p T of the exiting parton. The so-called unintegratedPDFs (UPDFs) D k (x, p T , Q) would be more suitable for the purpose, leading tohigher-quality QCD calculations. UPDFs are, however, more complicated to handle,both numerically and theoretically. (It is still a challenge to construct aparton-shower MC based consistently on the theoretically well defined UPDFs.)Another interesting " entanglement " of the evolution of PDFs on one side and ofthe parton shower (PS) MC on the other side is also present in the modeling ofthe showering of the incoming hadron — mostly for technical reasons andconvenience. The Markovian nature of the QCD evolution can be exploited directlyin the PS MC, where partons split/decay as long as there is enough energy todissipate (final state) or the upper boundary Q of the phase space is hit(initial state). The multiparton distribution in such a MC is a product of theevolution kernels. However, such a direct Markovian MC simulation of a shower ishopelessly inefficient in the initial state, because the hard process acceptsonly certain types * Supported in part by the EU grant MTKD-CT-2004-510126, inpartnership with the CERN Physics Department.CERNhep-ph/0509178IFJPAN-V-05-09CERN-PH-TH-2005-146CERN-PH-TH-2005-146IFJPAN-V-2005-09oai:cds.cern.ch:8850532005-09-18
spellingShingle Particle Physics - Phenomenology
Jadach, S.
Skrzypek, M.
Constrained non-Markovian Monte Carlo modelling of the evolution equation in QCD
title Constrained non-Markovian Monte Carlo modelling of the evolution equation in QCD
title_full Constrained non-Markovian Monte Carlo modelling of the evolution equation in QCD
title_fullStr Constrained non-Markovian Monte Carlo modelling of the evolution equation in QCD
title_full_unstemmed Constrained non-Markovian Monte Carlo modelling of the evolution equation in QCD
title_short Constrained non-Markovian Monte Carlo modelling of the evolution equation in QCD
title_sort constrained non-markovian monte carlo modelling of the evolution equation in qcd
topic Particle Physics - Phenomenology
url http://cds.cern.ch/record/885053
work_keys_str_mv AT jadachs constrainednonmarkovianmontecarlomodellingoftheevolutionequationinqcd
AT skrzypekm constrainednonmarkovianmontecarlomodellingoftheevolutionequationinqcd

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