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NNPDF is the acronym used to identify the
parton distribution functions In particle physics, the parton model is a model of hadrons, such as protons and neutrons, proposed by Richard Feynman. It is useful for interpreting the cascades of radiation (a parton shower) produced from quantum chromodynamics (QCD) processes ...
from the NNPDF Collaboration. NNPDF parton densities are extracted from global fits to data based on a combination of a
Monte Carlo method Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be ...
for uncertainty estimation and the use of
neural networks A neural network is a group of interconnected units called neurons that send signals to one another. Neurons can be either Cell (biology), biological cells or signal pathways. While individual neurons are simple, many of them together in a netwo ...
as basic interpolating functions.


Methodology

The NNPDF approach can be divided into four main steps: * The generation of a large sample of Monte Carlo replicas of the original experimental data, in a way that central values, errors and correlations are reproduced with enough accuracy. * The training (minimization of the \chi^2) of a set of PDFs parametrized by
neural network A neural network is a group of interconnected units called neurons that send signals to one another. Neurons can be either biological cells or signal pathways. While individual neurons are simple, many of them together in a network can perfor ...
s on each of the above MC replicas of the data. PDFs are parametrized at the initial evolution scale Q^_ and then evolved to the experimental data scale Q^2 by means of the
DGLAP The Dokshitzer–Gribov–Lipatov–Altarelli–Parisi (DGLAP) evolution equations are equations in QCD describing the variation of parton distribution functions with varying energy scales. Experimentally observed scaling violation in deep inelast ...
equations. Since the PDF parametrization is redundant, the minimization strategy is based in
genetic algorithm In computer science and operations research, a genetic algorithm (GA) is a metaheuristic inspired by the process of natural selection that belongs to the larger class of evolutionary algorithms (EA). Genetic algorithms are commonly used to g ...
s as well as gradient descent based minimizers. * The neural network training is stopped dynamically before entering into the overlearning regime, that is, so that the PDFs learn the physical laws which underlie experimental data without fitting simultaneously statistical noise. * Once the training of the MC replicas has been completed, a set of statistical estimators can be applied to the set of PDFs, in order to assess the statistical consistency of the results. For example, the stability with respect PDF parametrization can be explicitly verified. The set of N_ PDF sets (trained neural networks) provides a representation of the underlying PDF probability density, from which any statistical estimator can be computed.


Example

The image below shows the
gluon A gluon ( ) is a type of Massless particle, massless elementary particle that mediates the strong interaction between quarks, acting as the exchange particle for the interaction. Gluons are massless vector bosons, thereby having a Spin (physi ...
at small-x from
the NNPDF1.0 analysis
available throug
the LHAPDF interface
File:Gluon log ref.jpg, The NNPDF1.0 gluon


Releases

The NNPDF releases are summarised in the following table: All PDF sets are available through the LHAPDF interface and in th
NNPDF webpage


References


External links


The NNPDF Collaboration homepageThe NNPDF1.0 analysisThe NNPDF Non-Singlet analysisNNPDF3.1 releaseNNPDF latest fitting codeThe LHAPDF interface
{{Authority control Computational particle physics Physics software