NNPDF

NNPDF, short for Neural Network Parton Distribution Functions, is a collaboration that produces parton distribution functions (PDFs) for the proton used in high-energy physics calculations. The goal is to determine the proton's parton content with minimal bias and realistic uncertainties by employing neural networks as flexible parameterizations and Monte Carlo methods to propagate experimental errors.

Its methodology uses neural networks to represent each parton flavor as a function of the momentum fraction x and the scale Q^2. Networks are trained on a broad experimental data set, with uncertainties propagated by generating a large ensemble of Monte Carlo replicas and fitting each replica independently. Regularization and cross-validation mitigate overfitting, and sum rules enforce momentum conservation and correct quark counting. Fits are performed at LO, NLO, and NNLO in perturbative QCD.

Outputs and availability: The resulting PDFs include gluons and quarks (and antiquarks) over a range of x and Q^2, with uncertainties from the replica ensemble. They are publicly available through LHAPDF and are widely used in collider phenomenology for predictions such as W/Z production and jet processes.

History and significance: Established to reduce model bias from fixed functional forms, NNPDF has released multiple generations of PDF sets and remains a major contributor to global PDF analyses, complementing other groups.