I review recent progress in the NNPDF global analyses of parton distributions (PDFs) focusing on developments contributing to its new upcoming release: NNPDF4.0. The NNPDF4.0 determination represents unprecedented progress in three main directions: i) the systematic inclusion of LHC Run II data at 13 TeV and of new processes from dijets to single top distributions, ii) the deployment of state-of-the-art machine learning algorithms, from automated hyperparameter optimisation to stochastic gradient descent training; and iii) the complete statistical validation of PDF uncertainties, both in the data and extrapolation regions, by means of closure and future tests. Other methodological improvements in NNPDF4.0 include strict PDF positivity, integrability constraints at small-$x$, and deuteron and heavy nuclear corrections. I present representative results from NNPDF4.0 and assess its impact on open issues such as the light anti-quark asymmetry and the charm content of protons.
Parton Distribution Functions (PDFs) model the parton content of the proton. Among the many collaborations which focus on PDF determination, NNPDF pioneered the use of Neural Networks to model the probability of finding partons (quarks and gluons) inside the proton with a given energy and momentum. In this proceedings we make use of state of the art techniques to modernize the NNPDF methodology and study different models and optimizers in order to improve the quality of the PDF: improving both the quality and efficiency of the fits. We also present the evolutionary_keras library, a Keras imple…
As data become more precise, estimating theoretical uncertainties in global PDF determinations is likely to become increasingly necessary to obtain correspondingly precise PDFs. Here we present a next generation of global proton PDFs (NNPDF4.0) that include theoretical uncertainties due to the use of heavy nuclear and deuteron data in the fit. We estimate these uncertainties by comparing the values of the nuclear observables computed with the nuclear PDFs against those computed with proton PDFs. For heavy nuclear PDFs we use the nuclear nNNPDF2.0 set, while for deuteron PDFs we develop an iter…
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 methodology through hyperparameter optimisation, leading to an efficient fitting algorithm built upon stochastic gradient descent. We use NNLO QCD calculations and account for NLO electroweak corrections and nuclear uncertainties. Theoretical improvements in the PDF description include a systematic implementation of positivity constraints and integrability of sum …
The projection onto the Light-Front of a Minkowski space Faddeev-Bethe-Salpeter equation model truncated at the valence level is applied to study the proton structure with constituent quarks. The dynamics of the model has built-in: (i) a bound diquark brought by a contact interaction, and (ii) the separation by Λ_QCD of the infrared and ultraviolet interaction regions. The model parameters are fine tuned to reproduce the proton Dirac electromagnetic form factor and mass. From that, the non-polarized longitudinal and transverse momentum distributions were computed. The results for the evolved n…
We discuss a test of the generalization power of the methodology used in the determination of parton distribution functions (PDFs). The "future test" checks whether the uncertainty on PDFs, in regions in which they are not constrained by current data, are compatible with future data. The test is performed by using the current optimized methodology for PDF determination, but with a limited dataset, as available in the past, and by checking whether results are compatible within uncertainty with the result found using a current more extensive dataset. We use the future test to assess the generali…
This paper presents perturbative QCD predictions of the electron charge asymmetry for the inclusive $W^{\pm}+X \rightarrow e^{\pm} ν+X$ production in proton-proton (pp) collisions. Perturbative QCD calculations are performed at next-to-next-to-leading order (NNLO) accuracy by using different parton distribution function (PDF) models at 8 TeV, 13 TeV, and 14 TeV center-of-mass energies of the CERN LHC pp collisions. The NNLO calculations are performed for the electrons to have transverse momentum more than 20 GeV in the forward electron pseudorapidity region $2.0 \leq η_{e} \leq 4.25$. The NNLO…
We evaluate the uncertainties due to nuclear effects in global fits of proton parton distribution functions (PDFs) that utilise deep-inelastic scattering and Drell-Yan data on deuterium targets. To do this we use an iterative procedure to determine proton and deuteron PDFs simultaneously, each including the uncertainties in the other. We apply this procedure to determine the nuclear uncertainties in the SLAC, BCDMS, NMC and DYE866/NuSea fixed target deuteron data included in the NNPDF3.1 global fit. We show that the effect of the nuclear uncertainty on the proton PDFs is small, and that the in…
Description of Charged\text{-}Particle Multiplicity Distributions in High\text{-}Energy Proton\text{-}Proton Collisions Based on a Two-Component Model and Examination of Parton Distribution Functions
Analytic derivation of the next-to-leading order proton structure function $F_2^p(x, Q^2)$ based on the Laplace transformation
An analytical solution based on the Laplace transformation technique for the DGLAP evolution equations is presented at next-to-leading order accuracy in perturbative QCD. This technique is also applied to extract the analytical solution for the proton structure function, $F_2^p(x, Q^2)$ , in the Laplace $s$ -space. We present the results for the separate parton distributions for all parton species, including valence quark densities, the anti-quark and strange sea parton distribution functions (PDFs), and the gluon distribution. We successfully compare the obtained parton distribution functions…
In this work, using the Laplace transformation technique we present our results for non-singlet quark distributions as well as nucleon structure function $F_2(x,Q^2)$ in unpolarized case at next-to-next-to-leading order (NNLO) QCD accuracy. We shall particularly compare our results for the sets of valence-quark parton distribution functions with the contemporary collaborations like CT14, CT18, MMHT14, MKAM16 and NNPDF. To construct the nucleon structure function we employ the expansion of Jacobi polynomials which is a suitable transform to convert the results of non-singlet structure function …
