# Determination of Parton Distribution Functions

### *Group members:* Maria Ubiali, Robert Thorne

*Group members:*

In order to predict the results of any hard-scattering process where hadrons are the initial-state colliding particles, it is necessary to know the parton distributions within the hadrons, that parametrize the hadrons in terms of their elementary constituents, quarks and gluon.

We are leading members of the Neural-Network-PDFs (NNPDF) and the Martin-Stirling-Thorne-Watt (MSTW) collaborations, which are two of the major players involved in the determination of parton distribution functions (PDFs) from all available data from electron-proton (e.g. HERA) and proton-(anti)proton (e.g. Tevatron and LHC) colliders, by using next-to-next-to-leading order (NNLO) perturbative QCD. The determination of PDFs in the context of global QCD analyses leads also to the precise determination of the QCD coupling αS and other physical parameters such as the mass of the electroweak bosons and the Weinberg angle.

In the midst of the LHC era, it is paramount to precisely determine the PDFs of the protons, whose uncertainty is a limiting factor in the accuracy of QCD theoretical predictions. Work is done on the inclusion of new precise LHC measurements that provide a major constraint to PDFs as well as on theoretical improvements to standard perturbation theory adopted in parton fits.

The NNPDF collaboration has introduced a completely new approach in the determination of PDFs based on the use of Monte Carlo sampling techniques in the functional space PDFs and on the use of Neural Networks as unbiased parametrization for each independent parton distribution. We have recently produced a new set of parton distributions, the NNPDF2.3, which is the first available NLO and NNLO fit including the early LHC data arxiv:1207.1303. A new release, with many more LHC data and an improved fitting methodology, the NNPDF3.0, is to be released soon.

Further information and PDF codes can be found on the NNPDF page and MSTW page at HepForge.

(Top figure) Fit of the gluon distribution at Q^2 = 2 GeV^2 in the NNPDF2.3 NNLO fit. Each green line is the best fit for one of the 100 NNPDF Monte Carlo replica. The average is given by the red line, the 1-sigma contour is given by the solid blue line

(Bottom figure) Comparison of the gluon-gluon luminosity determined at NNLO in the NNPDF2.3, MSTW2008 and CT10 global analyses of parton distributions. Results are normalized to the MSTW2008 central value.