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We examine the dependence of parton distribution functions (PDFs) on the value of the QCD coupling strength $\alpha_{s}(M_{Z})$. We explain a simple method that is rigorously valid in the quadratic approximation normally applied in PDF…
We discuss the statistical properties of parton distributions within the framework of the NNPDF methodology. We present various tests of statistical consistency, in particular that the distribution of results does not depend on the…
We outline the historical development of MRST/MSTW parton distribution functions (PDFs), and clarify how they should be regarded when compared to the most up-to-date 2008 MSTW sets, noting which sets are now obsolete and the reasons why.
A method to approximate continuous multi-dimensional probability density functions (PDFs) using their projections and correlations is described. The method is particularly useful for event classification when estimates of systematic…
The parton distribution functions (PDFs) of the proton, a necessary input to almost all theory predictions for hadron colliders, are reviewed in this document. An introduction to the PDF determination by global analyses of the main PDF…
Study of parton distribution functions (PDFs) has led to a finer cognisance of the structure of partons in hadrons and the proton structure functions in deep inelastic scattering (DIS). PDFs are instrumental in predicting results for most…
We present a new procedure to determine Parton Distribution Functions (PDFs), based on Markov Chain Monte Carlo (MCMC) methods. The aim of this paper is to show that we can replace the standard $\chi^2$ minimization by procedures grounded…
We present a Mathematica interface for handling the parton distribution functions of the NNDPF Collaboration, available from the NNPDF hepforge website http://nnpdf.hepforge.org/. As a case study we briefly summarise the first PDF set which…
We present recent progress within the NNPDF parton analysis framework. After a brief review of the results from the DIS NNPDF analysis, NNPDF1.0, we discuss results from an updated analysis with independent parametrizations for the strange…
Beyond leading-order, perturbative QCD requires a choice of factorisation scheme to define the parton distribution functions (PDFs) and hard-process cross-section. The modified minimal-subtraction ($\overline{\mathrm{MS}}$) scheme has long…
An important limitation in current fits of parton distribution functions (PDFs) is that PDF uncertainties do not include any source of theoretical uncertainty. Here we present a general method for incorporating theoretical uncertainties…
We review the current status of spin-averaged and spin-dependent parton distribution functions (PDFs) of the nucleon. After presenting the formalism used to fit PDFs in modern global data analyses, we discuss constraints placed on the PDFs…
Multi-parton distribution functions (mPDFs) are non-perturbative objects that are important in the prediction of multiple scattering rates at hadron colliders. In the case where the scales associated with all partons in the mPDF are the…
We present a new set of parton distribution functions (PDFs) based on a fully global dataset and machine learning techniques: NNPDF4.0. We expand the NNPDF3.1 determination with 44 new datasets, mostly from the LHC. We derive a novel…
We provide an assessment of the state of the art in various issues related to experimental measurements, phenomenological methods and theoretical results relevant for the determination of parton distribution functions (PDFs) and their…
We review various methods used to estimate uncertainties in quantum correlation functions, such as parton distribution functions (PDFs). Using a toy model of a PDF, we compare the uncertainty estimates yielded by the traditional Hessian and…
A "meta-analysis" is a method for comparison and combination of nonperturbative parton distribution functions (PDFs) in a nucleon obtained with heterogeneous procedures and assumptions. Each input parton distribution set is converted into a…
The interpretation of LHC measurements requires a careful estimate of various sources of uncertainties that affect theoretical calculations. In this contribution, we present the PDF4LHC Working Group recommendations for the usage of sets of…
In this contribution we present a status report on the recent progress towards an analysis of nuclear parton distribution functions (nPDFs) using the NNPDF methodology. We discuss how the NNPDF fitting approach can be extended to account…
We provide an analysis of the x-dependence of the bare unpolarized, helicity and transversity iso-vector parton distribution functions (PDFs) from lattice calculations employing (maximally) twisted mass fermions. The x-dependence of the…