135 research outputs found
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
Solving QCD evolution equations in rapidity space with Markovian Monte Carlo
This work covers methodology of solving QCD evolution equation of the parton
distribution using Markovian Monte Carlo (MMC) algorithms in a class of models
ranging from DGLAP to CCFM. One of the purposes of the above MMCs is to test
the other more sophisticated Monte Carlo programs, the so-called Constrained
Monte Carlo (CMC) programs, which will be used as a building block in the
parton shower MC. This is why the mapping of the evolution variables (eikonal
variable and evolution time) into four-momenta is also defined and tested. The
evolution time is identified with the rapidity variable of the emitted parton.
The presented MMCs are tested independently, with ~0.1% precision, against the
non-MC program APCheb especially devised for this purpose.Comment: version compatible with with the erratum in Acta Physica Polonic
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
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
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
Markovian MC simulation of QCD evolution at NLO level with minimum k_T
We present two Monte Carlo algorithms of the Markovian type which solve the
modified QCD evolution equations at the NLO level. The modifications with
respect to the standard DGLAP evolution concern the argument of the strong
coupling constant alpha_S. We analyze the z - dependent argument and then the
k_T - dependent one. The evolution time variable is identified with the
rapidity. The two algorithms are tested to the 0.05% precision level. We find
that the NLO corrections in the evolution of parton momentum distributions with
k_T - dependent coupling constant are of the order of 10 to 20%, and in a small
x region even up to 30%, with respect to the LO contributions.Comment: 32 pages, 9 pdf figure
Two real parton contributions to non-singlet kernels for exclusive QCD DGLAP evolution
Results for the two real parton differential distributions needed for
implementing a next-to-leading order (NLO) parton shower Monte Carlo are
presented. They are also integrated over the phase space in order to provide
solid numerical control of the MC codes and for the discussion of the
differences between the standard factorization and Monte Carlo
implementation at the level of inclusive NLO evolution kernels. Presented
results cover the class of non-singlet diagrams entering into NLO kernels. The
classic work of Curci-Furmanski-Pertonzio was used as a guide in the
calculations.Comment: 34 pages, 3 figure
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