Parton distribution functions and theory parameters: an NNPDF perspective
University of Edinburgh（爱丁堡大学）；Max Planck Institute for Physics（马克斯·普朗克物理研究所）；University of Jyvaskyla（于韦斯屈莱大学）；Helsinki Institute of Physics（赫尔辛基物理研究所）；Vrije Universiteit（自由大学）；Nikhef Theory Group（尼赫夫理论组）；University of Cambridge（剑桥大学）
Richard D. Ball, Tommaso Giani, Felix Hekhorn, Jaco ter Hoeve, Tanjona R. Rabemananjara, Juan Rojo, Roy Stegeman, Maria Ubiali
备注：
Submitted for publication by Elsevier Ltd. in a Physics Reports collection of papers on Electroweak Precision Physics, edited by F. Bedeschi, A. Kotwal M. Ramsey-Musolf, C. Vellidis, and D. Wackeroth
Parton Distribution Functions (PDFs) are a key ingredient in theoretical predictions for Large Hadron Collider (LHC) observables and play a central role in the extraction of precision Standard Model (SM) and Beyond the SM (BSM) parameters from LHC data. Recent analyses demonstrate that the determination of fundamental SM parameters such as $α_s(m_Z)$, $m_W$, $m_t$, and $\sin^2θ_W$ is strongly influenced by the choice of input PDFs. In this contribution, we present the status and challenges of PDF determination from the NNPDF perspective, both in stand-alone fits and in joint extractions with (B)SM parameters. We place particular emphasis on results for $α_s(m_Z)$, $m_t$, and Wilson coefficients in the SM Effective Field Theory (SMEFT) framework.
We discuss the main features of the recent NNPDF2.1 NLO set, a determination of parton distributions from a global set of hard scattering data using the NNPDF methodology including heavy quark mass effects. We present the implications for LHC observables of this new PDF set. Then we briefly review recent NNPDF progress towards NNLO sets, and in particular the impact of the treatment of fixed target NMC data on NNLO Higgs cross sections.
We present a method developed by the NNPDF Collaboration that allows the inclusion of new experimental data into an existing set of parton distribution functions without the need for a complete refit. A Monte Carlo ensemble of PDFs may be updated by assigning each member of the ensemble a unique weight determined by Bayesian inference. The reweighted ensemble therefore represents the probability density of PDFs conditional on both the old and new data. This method is applied to the inclusion of W-lepton asymmetry data into the NNPDF2.1 fit producing a new PDF set, NNPDF2.2.
The full exploitation of the increasingly precise LHC measurements is essential in order to reduce the uncertainty of theoretical predictions at hadron colliders. The NNPDF2.3 fit was the first PDF determination including the effect of the early LHC data. Here the new NNPDF3.0 PDF set is announced and its main features are presented. The novel NNPDF analysis is based on an improved fitting methodology, statistically validated by closure tests. Over a thousand new data points are included, both the recent HERA II measurements and a wide set of new LHC data. In this contribution details on the e…
Recently a new set of Parton Distribution Functions (NNPDF1.2) has been produced and released by the NNPDF Collaboration. The inclusion of dimuon data in the analysis allows a determination of the strange content of the proton with faithful uncertainty estimation together with a precision determination of electroweak parameters. In this contribution, we discuss some of the implications of the NNPDF1.2 set, and in particular of its uncertainty determination of the strange PDFs, for LHC phenomenology. First of all, we study the impact on the electroweak boson production cross-section, with speci…
We present sets of parton distribution functions (PDFs), based on the NNPDF3.0 family, which include the photon PDF from the NNPDF2.3QED sets, and leading-order QED contributions to the DGLAP evolution as implemented in the public code APFEL. The aim is to combine our state-of-the-art determination of quark and gluon PDFs with the so far only direct determination of the photon PDF from LHC data. In addition, the use of APFEL allowed us to employ a solution of the DGLAP equation that, differently from that used for the NNPDF2.3QED sets, includes QED corrections in a more accurate way. We briefl…
We present the implementation within the Pythia8 event generator of a set of parton distributions based on NNPDF methodology. We construct a set of leading-order parton distributions with QED corrections, NNPDF2.3QED LO set, based on the same data as the previous NNPDF2.3 NLO and NNLO PDF sets. We compare this PDF set to its higher-order counterparts, we discuss its implementation as an internal set in Pythia8, and we use it to study some of the phenomenological implications of photon-initiated contributions for dilepton production at hadron colliders.
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 for the dependence on the atomic mass number $A$, and introduce novel algorithms to improve the training of the neural network parameters within the NNPDF framework. Finally, we present preliminary results of a nPDF fit to neutral current deep-inelastic lepton-nucleus scattering data, and demonstrate how one can validate the new fitting methodology by means of…
We present a set of parton distribution functions (PDFs), based on the NNPDF2.3 set, which includes a photon PDF, and QED contributions to parton evolution. We describe the implementation of the combined QCD+QED evolution in the NNPDF framework. We then provide a first determination of the full set of PDFs based on deep-inelastic scattering data and LHC data for W and Z/gamma* Drell-Yan production, using leading-order QED and NLO or NNLO QCD. We compare the ensuing NNPDF2.3QED PDF set to the older MRST2004QED set. We perform a preliminary investigation of the phenomenological implications of N…
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 includes all relevant LHC data, NNPDF2.3, and demonstrate the use of our new Mathematica interface.
I investigate the behavior of spin-dependent parton distribution functions in the regions of small and large momentum fractions $x$. I present a systematic comparison between predictions for relevant observables obtained with various models of nucleon spin structure and a recent global analysis of spin-dependent distributions, NNPDFpol1.1. Together with its unpolarized counterpart, NNPDF2.3, they form a mutually consistent set of parton distributions. Because they include most of the available experimental information, and are determined with a minimally biased methodology, these are especiall…
I present a determination of longitudinally-polarized parton distribution functions of the proton from inclusive deep-inelastic scattering data: NNPDFpol1.0+. This determination, based on the NNPDF methodology, upgrades a previous analysis, NNPDFpol1.0, in two respects: first, it includes all new data sets which have recently become available from the COMPASS experiment at CERN and from the E93-009, EG1-DVCS and E06-014 experiments at JLAB; second, it uses the state-of-the-art unpolarized parton set NNPDF3.0 as a baseline for the reconstruction of fitted observables and for the determination o…
We present the software framework underlying the NNPDF4.0 global determination of parton distribution functions (PDFs). The code is released under an open source licence and is accompanied by extensive documentation and examples. The code base is composed by a PDF fitting package, tools to handle experimental data and to efficiently compare it to theoretical predictions, and a versatile analysis framework. In addition to ensuring the reproducibility of the NNPDF4.0 (and subsequent) determination, the public release of the NNPDF fitting framework enables a number of phenomenological application…
We present preliminary results on the determination of spin-dependent, or polarised, Parton Distribution Functions (PDFs) from all relevant inclusive polarised DIS data. The analysis is performed within the NNPDF approach, which provides a faithful and statistically sound representation of PDFs and their uncertainties. We describe how the NNPDF methodology has been extended to the polarised case, and compare our results with other recent polarised parton sets. We show that polarised PDF uncertainties can be sizeably underestimated in standard determinations, most notably for the gluon.
The method of closure testing for analysing the effectiveness of a PDF fitting procedure is discussed. In order to pass a closure test, a fitting methodology must be able to reproduce a known generating function in a fit to an ideal pseudo-dataset generated by that PDF up to the level of experimental uncertainty in the data. Here we present an initial study of the closure property of the NNPDF fitting methodology. An idealised pseudo-dataset is generated by a set of toy PDFs that differ substantially from previous NNPDF determinations. In a fit to this pseudodata, the NNPDF methodology is show…
We study the potential impact of inclusive deep-inelastic scattering data from a future electron-ion collider (EIC) on longitudinally polarized parton distribution (PDFs). We perform a PDF determination using the NNPDF methodology, based on sets of deep-inelastic EIC pseudodata, for different realistic choices of the electron and proton beam energies. We compare the results to our current polarized PDF set, NNPDFpol1.0, based on a fit to fixed-target inclusive DIS data. We show that the uncertainties on the first moments of the polarized quark singlet and gluon distributions are substantially …
We study the impact of new open charm muoproduction data from COMPASS and preliminary W production data from STAR on NNPDFpol1.0, the first unbiased set of polarized parton distributions recently delivered by the NNPDF Collaboration and based on inclusive Deep-Inelastic Scattering data only. The information contained in the new data sets is incorporated in our Monte Carlo parton determination via Bayesian reweighting, a method based on statistical inference which avoids the need for a global refitting. We explicitly show to which extent COMPASS and STAR data can improve our knowledge of gluon …
We present a determination of a set of polarized parton distributions (PDFs) of the nucleon, at next-to-leading order, from a global set of longitudinally polarized deep-inelastic scattering data: NNPDFpol1.0. The determination is based on the NNPDF methodology: a Monte Carlo approach, with neural networks used as unbiased interpolants, previously applied to the determination of unpolarized parton distributions, and designed to provide a faithful and statistically sound representation of PDF uncertainties. We present our dataset, its statistical features, and its Monte Carlo representation. We…
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…
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 d…
We present the first determination of parton distributions of the nucleon at NLO and NNLO based on a global data set which includes LHC data: NNPDF2.3. Our data set includes, besides the deep inelastic, Drell-Yan, gauge boson production and jet data already used in previous global PDF determinations, all the relevant LHC data for which experimental systematic uncertainties are currently available: ATLAS and LHCb W and Z lepton rapidity distributions from the 2010 run, CMS W electron asymmetry data from the 2011 run, and ATLAS inclusive jet cross-sections from the 2010 run. We introduce an impr…
We present a method for incorporating the information contained in new datasets into an existing set of parton distribution functions without the need for refitting. The method involves reweighting the ensemble of parton densities through the computation of the chi-square to the new dataset. We explain how reweighting may be used to assess the impact of any new data or pseudodata on parton densities and thus on their predictions. We show that the method works by considering the addition of inclusive jet data to a DIS+DY fit, and comparing to the refitted distribution. We then use reweighting t…
The choice of data that enters a global QCD analysis can have a substantial impact on the resulting parton distributions and their predictions for collider observables. One of the main reasons for this has to do with the possible presence of inconsistencies, either internal within an experiment or external between different experiments. In order to assess the robustness of the global fit, different definitions of a conservative PDF set, that is, a PDF set based on a maximally consistent dataset, have been introduced. However, these approaches are typically affected by theory biases in the sele…
We present a determination of the parton distributions of the nucleon from a global set of hard scattering data using the NNPDF methodology including heavy quark mass effects: NNPDF2.1. In comparison to the previous NNPDF2.0 parton determination, the dataset is enlarged to include deep--inelastic charm structure function data. We implement the FONLL-A general-mass scheme in the FastKernel framework and assess its accuracy by comparison to the Les Houches heavy quark benchmarks. We discuss the impact on parton distributions of the treatment of the heavy quark masses, and we provide a determinat…
We respond to the criticism raised by Courtoy et al., in which the faithfulness of the NNPDF4.0 sampling is questioned and an under-estimate of the NNPDF4.0 PDF uncertainties is implied. We list, correct, and clarify in detail a number of inaccurate or misleading claims that are made in this Reference. Specifically, we explain and explicitly demonstrate why the central value of the PDF distribution does not generally coincide with the absolute minimum of the $χ^{2}$ to the data. We examine some PDFs that have been constructed in the above study and claimed to be "good solutions": we show that …
In this contribution we briefly report on the progress and open problems in parton distribution functions (PDFs), with emphasis on their implications for LHC phenomenology. Then we study the impact of the recent ATLAS and CMS W lepton asymmetry data on the NNPDF2.1 parton distributions. We show that these data provide the first constrains on PDFs from LHC measurements.
We discuss the Bayesian approach to the solution of inverse problems and apply the formalism to analyse the closure tests performed by the NNPDF collaboration. Starting from a comparison with the approach that is currently used for the determination of parton distributions (PDFs) by the NNPDF collaboration, we discuss some analytical results that can be obtained for linear problems and use these results as a guidance for the more complicated non-linear problems. We show that, in the case of Gaussian distributions, the posterior probability density of the parametrized PDFs is fully determined b…
We discuss the determination of the parton substructure of hadrons by casting it as a peculiar form of pattern recognition problem in which the pattern is a probability distribution, and we present the way this problem has been tackled and solved. Specifically, we review the NNPDF approach to PDF determination, which is based on the combination of a Monte Carlo approach with neural networks as basic underlying interpolators. We discuss the current NNPDF methodology, based on genetic minimization, and its validation through closure testing. We then present recent developments in which a hyperop…
We show how an inaccurate determination of experimental uncertainty correlations in high-precision LHC measurements may undermine the reliability of the associated $χ^2$. We formulate the problem rigorously, and devise a regularisation procedure that increases the stability of the $χ^2$ by altering the covariance matrix of the measurement as little as possible. We apply the procedure to the NNPDF4.0 global analysis of parton distribution functions that utilises a large amount of LHC measurements. We find that the regularised $χ^2$ of the NNPDF4.0 determination is lowered by about $3σ$, without…
Electroweak corrections to hadron collider processes become relevant at the level of precision reached by present-day LHC experiments. We provide a preliminary discussion of the impact of electroweak corrections to parton distributions, concentrating on electrodynamics corrections to parton evolution equations, and showing a preliminary assessment of their impact. Furthermore, we determine the parton distribution function of the photon from deep inelastic scattering data using the NNPDF methodology.
We discuss the current minimisation strategies adopted by research projects involving the determination of parton distribution functions (PDFs) and fragmentation functions (FFs) through the training of neural networks. We present a short overview of a proton PDF determination obtained using the covariance matrix adaptation evolution strategy (CMA-ES) optimisation algorithm. We perform comparisons between the CMA-ES and the standard nodal genetic algorithm (NGA) adopted by the NNPDF collaboration.
We present updated predictions for the cross-sections for pair production of squarks and gluinos at the LHC Run II. First of all, we update the calculations based on NLO+NLL partonic cross-sections by using the NNPDF3.0NLO global analysis. This study includes a full characterization of theoretical uncertainties from higher orders, PDFs and the strong coupling. Then, we explore the implications for this calculation of the recent NNPDF3.0 PDFs with NLO+NLL threshold resummation. We find that the shift in the results induced by the threshold-improved PDFs is within the total theory uncertainty ba…
Recent measurements of top quark pair production cross section, which is performed at the LHC and the Tevatron collider, are studied using Hessian profiling technique to obtain their impact on the parton distribution functions (PDFs). The top quark production data covers different center-of-mass energies $\sqrt{s}$= 1.96, 5.02, 7, 8 and 13 TeV in either $pp$ or $p\bar{p}$ collisions. It is explained how the Hessian profiling method may be used to assess the impact of these new data on PDFs and consequently on their predictions. In this research, the impact of recent measurements of top quark p…
Modern parton distribution function fits require an accurate treatment of heavy quark mass effects. In this contribution, we discuss how the FONLL general-mass variable flavour number scheme can be extended to allow for the possibility of a fitted charm PDF. We present a first estimate of the impact of a fitted charm contribution in the FONLL structure functions, and we discuss the development towards including a fitted charm PDF in the NNPDF framework.
The NNPDF collaboration has recently presented NNPDF3.1, a new determination of the parton distribution functions (PDFs) of the proton including a number of new data, some of which are particularly sensitive to the gluon PDF at large x. In this contribution, we present the results of two new analyses based on NNPDF3.1. First, we study the impact of the ATLAS 2011 7 TeV inclusive jet data on the gluon PDF including different rapidity bins. Second, we quantitatively compare the constraints provided by all measurements sensitive to the large-x gluon PDF, namely inclusive jet cross sections, the t…
We present a determination of the parton distributions of the nucleon from a global set of hard scattering data using the NNPDF methodology at LO and NNLO in perturbative QCD, thereby generalizing to these orders the NNPDF2.1 NLO parton set. Heavy quark masses are included using the so-called FONLL method, which is benchmarked here at NNLO. We demonstrate the stability of PDFs upon inclusion of NNLO corrections, and we investigate the convergence of the perturbative expansion by comparing LO, NLO and NNLO results. We show that the momentum sum rule can be tested with increasing accuracy at LO,…
We review the next generation global PDF sets: NNPDF3.0, MMHT14 and CT14. We describe the global datasets, particularly the new data from LHC Run 1, recent developments in QCD theory and PDF methodology, improvements in combination and delivery, and future prospects for parton determination at Run 2.
We present the first unbiased determination of parton distribution functions (PDFs) with electroweak corrections. The aim of this thesis is to provide an exhaustive description of the theoretical framework and the technical implementation which leads to the determination of a set of PDFs which includes the photon PDF and quantum electrodynamics (QED) contributions to parton evolution. First, we introduce and motivate the need of including electroweak corrections to PDFs, providing phenomenological examples and presenting an overview of the current state of the art in PDF fits. The theoretical …
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…
Since the first determination of a structure function many decades ago, all methodologies used to determine structure functions or parton distribution functions (PDFs) have employed a common prefactor as part of the parametrization. The NNPDF collaboration pioneered the use of neural networks to overcome the inherent bias of constraining the space of solution with a fixed functional form while still keeping the same common prefactor as a preprocessing. Over the years various, increasingly sophisticated, techniques have been introduced to counter the effect of the prefactor on the PDF determina…
Parton distribution functions (PDFs) with QED corrections extracted from the QED$\otimes$QCD DGLAP evolution equations in the framework of "valon" model. Our results for the PDFs with QED corrections in this phenomenological model are in good agreement with the newly related CT14QED global fit code [Phys. Rev. D93, 114015 (2016)] and APFEL (NNPDF2.3QED) [Computer Physics Communications 185, 1647 (2014)] program in a wide range of $x=[10^{-5}, 1]$ and $Q^2=[0.283, 10^8] \, {\rm GeV}^2$. The model calculations agree rather well with those codes. We also proposed the new method for studying the s…
We present a first determination of the nuclear parton distribution functions (nPDF) based on the NNPDF methodology: nNNPDF1.0. This analysis is based on neutral-current deep-inelastic structure function data and is performed up to NNLO in QCD calculations with heavy quark mass effects. For the first time in the NNPDF fits, the $χ^2$ minimization is achieved using stochastic gradient descent with reverse-mode automatic differentiation (backpropagation). We validate the robustness of the fitting methodology through closure tests, assess the perturbative stability of the resulting nPDFs, and com…
A determination of Parton Distribution Functions (PDFs) from a global fit to a dataset including measurements from the LHC has been performed. The determinations have been carried out according to the NNPDF methodology, leading to a fit minimising parametrisation bias and with an accurate account of PDF uncertainty. In this thesis the importance of QCD measurements at the LHC to PDF extraction are discussed, and we summarise some of the technical difficulties in their inclusion into PDF fits. A number of methods are presented that permit the efficient inclusion of these observables into PDF de…
We extract two nonsinglet nucleon Parton Distribution Functions from lattice QCD data for reduced Ioffe-time pseudodistributions. We perform such analysis within the NNPDF framework, considering data coming from different lattice ensembles and discussing in detail the treatment of the different source of systematics involved in the fit. We introduce a recipe for taking care of systematics and use it to perform our extraction of light-cone PDFs.
We present a first global determination of spin-dependent parton distribution functions (PDFs) and their uncertainties using the NNPDF methodology: NNPDFpol1.1. Longitudinally polarized deep-inelastic scattering data, already used for the previous NNPDFpol1.0 PDF set, are supplemented with the most recent polarized hadron collider data for inclusive jet and $W$ boson production from the STAR and PHENIX experiments at RHIC, and with open-charm production data from the COMPASS experiment, thereby allowing for a separate determination of the polarized quark and anti-quark PDFs, and an improved de…
The proposed Large Hadron Electron Collider (LHeC) at CERN would bring Deep-Inelastic scattering into the unexplored TeV regime. The LHeC rich physics program, among other topics, includes both precision SM measurements to complement LHC physics as well as studies of QCD in the high energy limit. The present contribution reports on ongoing studies within the NNPDF framework towards the LHeC CDR. We study the impact of LHeC simulated data on PDF uncertainties, in particular the small-x gluon. We also assess the LHeC potential to disentangle between various scenarios of small-x QCD, including sa…
We present the MCscales approach for incorporating scale uncertainties in parton distribution functions (PDFs). The new methodology builds on the Monte Carlo sampling for propagating experimental uncertainties into the PDF space that underlies the NNPDF approach, but it extends it to the space of factorisation and renomalisation scales. A prior probability is assigned to each scale combinations set in the theoretical predictions used to obtain each PDF replica in the Monte Carlo ensemble and a posterior probability is obtained by selecting replicas that satisfy fit-quality criteria. Our approa…
Novel PDFs taking into account resummation-improved matrix elements, albeit only in the fit of a reduced data set, allow for consistent NLO+NLL calculations of slepton pair production at the LHC. We apply a factorisation method to this process that minimises the effect of the data set reduction, avoids the problem of outlier replicas in the NNPDF method for PDF uncertainties and preserves the reduction of the scale uncertainty. For Run II of the LHC, left-handed selectron/smuon, right-handed and maximally mixed stau production, we confirm that the consistent use of threshold-improved PDFs part…
In global QCD fits of parton distribution functions (PDFs), a large part of the estimated uncertainty on the PDFs originates from the choices of parametric functional forms and fitting methodology. We argue that these types of uncertainties can be underestimated with common PDF ensembles in high-stake measurements at the Large Hadron Collider and Tevatron. A fruitful approach to quantify these uncertainties is to view them as arising from sampling of allowed PDF solutions in a multidimensional parametric space. This approach applies powerful insights gained in recent statistical studies of lar…
We present a determination of the parton distributions of the nucleon from a global set of hard scattering data using the NNPDF methodology: NNPDF2.0. Experimental data include deep-inelastic scattering with the combined HERA-I dataset, fixed target Drell-Yan production, collider weak boson production and inclusive jet production. Next-to-leading order QCD is used throughout without resorting to K-factors. We present and utilize an improved fast algorithm for the solution of evolution equations and the computation of general hadronic processes. We introduce improved techniques for the training…
We use recent neutrino dimuon production data combined with a global deep-inelastic parton fit to construct a new parton set, NNPDF1.2, which includes a determination of the strange and antistrange distributions of the nucleon. The result is characterized by a faithful estimation of uncertainties thanks to the use of the NNPDF methodology, and is free of model or theoretical assumptions other than the use of NLO perturbative QCD and exact sum rules. Better control of the uncertainties of the strange and antistrange parton distributions allows us to reassess the determination of electroweak par…
We present a new set of parton distributions, NNPDF3.1, which updates NNPDF3.0, the first global set of PDFs determined using a methodology validated by a closure test. The update is motivated by recent progress in methodology and available data, and involves both. On the methodological side, we now parametrize and determine the charm PDF alongside the light quarks and gluon ones, thereby increasing from seven to eight the number of independent PDFs. On the data side, we now include the D0 electron and muon W asymmetries from the final Tevatron dataset, the complete LHCb measurements of W and …
We present a new regression model for the determination of parton distribution functions (PDF) using techniques inspired from deep learning projects. In the context of the NNPDF methodology, we implement a new efficient computing framework based on graph generated models for PDF parametrization and gradient descent optimization. The best model configuration is derived from a robust cross-validation mechanism through a hyperparametrization tune procedure. We show that results provided by this new framework outperforms the current state-of-the-art PDF fitting methodology in terms of best model s…
