782 research outputs found
Exact solutions of the QCD evolution equations using Monte Carlo method
We present the exact and precise (~0.1%) numerical solution of the QCD
evolution equations for the parton distributions in a wide range of and
using Monte Carlo (MC) method, which relies on the so-called Markovian
algorithm. We point out certain advantages of such a method with respect to the
existing non-MC methods. We also formulate a challenge of constructing
non-Markovian MC algorithm for the evolution equations for the initial state
QCD radiation with tagging the type and of the exiting parton. This seems
to be within the reach of the presently available computer CPUs and the
sophistication of the MC techniques
Non-Markovian Monte Carlo Algorithm for the Constrained Markovian Evolution in QCD
We revisit the challenging problem of finding an efficient Monte Carlo (MC)
algorithm solving the constrained evolution equations for the initial-state QCD
radiation. The type of the parton (quark, gluon) and the energy fraction x of
the parton exiting emission chain (entering hard process) are predefined, i.e.
constrained throughout the evolution. Such a constraint is mandatory for any
realistic MC for the initial state QCD parton shower. We add one important
condition: the MC algorithm must not require the a priori knowledge of the full
numerical exact solutions of the evolution equations, as is the case in the
popular ``Markovian MC for backward evolution''. Our aim is to find at least
one solution of this problem that would function in practice. Finding such a
solution seems to be definitely within the reach of the currently available
computer CPUs and the sophistication of the modern MC techniques. We describe
in this work the first example of an efficient solution of this kind. Its
numerical implementation is still restricted to the pure gluon-strahlung. As
expected, it is not in the class of the so-called Markovian MCs. For this
reason we refer to it as belonging to a class of non-Markovian MCs. We show
that numerical results of our new MC algorithm agree very well (to 0.2%) with
the results of the other MC program of our own (unconstrained Markovian) and
another non-MC program QCDnum16. This provides a proof of the existence of the
new class of MC techniques, to be exploited in the precision perturbative QCD
calculations for the Large Hadron Collider
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
reasonable.Comment: Contribution to HERA-LHC worksho
Solving constrained Markovian evolution in QCD with the help of the non-Markovian Monte Carlo
We present the constrained Monte Carlo (CMC) algorithm for the QCD evolution.
The constraint resides in that the total longitudinal energy of the emissions
in the MC and in the underlying QCD evolution is predefined (constrained). This
CMC implements exactly the full DGLAP evolution of the parton distributions in
the hadron with respect to the logarithm of the energy scale. The algorithm of
the CMC is referred to as the non-Markovian type. The non-Markovian MC
algorithm is defined as the one in which the multiplicity of emissions is
chosen randomly as the first variable and not the last one, as in the Markovian
MC algorithms. The former case resembles that of the fixed-order matrix element
calculations. The CMC algorithm can serve as an alternative to the so-called
backward evolution Markovian algorithm of Sjostrand, which is used for
modelling the initial-state parton shower in modern QCD MC event generators. We
test practical feasibility and efficiency of our CMC implementation in a series
of numerical exercises, comparing its results with those from other MC and
non-MC programs, in a wide range of Q and x, down to the 0.1% precision level.
In particular, satisfactory numerical agreement is found with the results of
the Markovian MC program of our own and the other non-MC program. The
efficiency of the new constrained MC is found to be quite good
Exclusive Monte Carlo modelling of NLO DGLAP evolution
The next-to-leading order (NLO) evolution of the parton distribution
functions (PDFs) in QCD is a common tool in the lepton-hadron and hadron-hadron
collider data analysis. The standard NLO DGLAP evolution is formulated for
inclusive (integrated) PDFs and done using inclusive NLO kernels. We report
here on the ongoing project, called KRKMC, in which NLO DGLAP evolution is
performed for the exclusive multiparton (fully unintegrated) distributions
(ePDFs) with the help of the exclusive kernels. These kernels are calculated
within the two-parton phase space for the non-singlet evolution, using
Curci-Furmanski-Petronzio factorization scheme. The multiparton distribution,
with multiple use of the exclusive NLO kernels, is implemented in the Monte
Carlo program simulating multi-gluon emission from single quark emitter. High
statistics tests ( events) show that the new scheme works
perfectly well in practice and, at the inclusive (integrated) level, is
equivalent with the traditional inclusive NLO DGLAP evolution. Once completed,
this new technique is aimed as a building block for the new more precise NLO
parton shower Monte Carlo, for W/Z production at LHC and for ep scattering, as
well as a starting point for other perturbative QCD based Monte Carlo projects.Comment: Contribution RADCOR 2009 Int. Symposiu
Markovian Monte Carlo program EvolFMC v.2 for solving QCD evolution equations
We present the program EvolFMC v.2 that solves the evolution equations in QCD
for the parton momentum distributions by means of the Monte Carlo technique
based on the Markovian process. The program solves the DGLAP-type evolution as
well as modified-DGLAP ones. In both cases the evolution can be performed in
the LO or NLO approximation. The quarks are treated as massless. The overall
technical precision of the code has been established at 0.05% precision level.
This way, for the first time ever, we demonstrate that with the Monte Carlo
method one can solve the evolution equations with precision comparable to the
other numerical methods.Comment: 38 pages, 9 Postscript figure
NLO corrections in the initial-state parton shower Monte Carlo
The decade-old technique of combining NLO-corrected hard process with
LO-level parton shower Monte Carlo is now mature and used in practice of the
QCD calculations in the LHC data analysis. The next step, its extension to an
NNLO-corrected hard process combined with the NLO-level parton shower Monte
Carlo, will require development of the latter component. It does not exist yet
in a complete form. In this note we describe recent progress in developing the
NLO parton shower for the initial-state hadron beams. The technique of adding
NLO corrections in the fully exclusive form (defined in recent years) is now
simplified and tested numerically, albeit for a limited set of NLO diagrams in
the evolution kernels.Comment: 8 pages, 5 figure
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