arXiv subjects

Aurore Courtoy

Publications and source records attributed to Aurore Courtoy.

At least 19 recordsLinked to original sources

arXiv2025

Fantômas: An analysis of parton distributions in a pion with Bézier parametrizations

We systematically explore the parametrization dependence of the Parton Distribution Functions (PDFs) to better quantify the true uncertainty from global QCD analyses. To achieve this, we employ a novel technique that automates the generation of polynomial parametrizations for PDFs using Bézier curves. This technique is implemented in a C++ module, named Fantômas, which is now included within the xFitter program. As an example, we examine the charged pion PDF. Our analysis reveals that the sea and gluon distributions in the pion are strongly correlated, and PDF solutions featuring a vanishing gluon and a large quark sea are still experimentally allowed.

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arXiv2025

Information Criteria for Selecting Parton Distribution Function Solutions

In data-driven determination of Parton Distribution Functions (PDFs) in global QCD analyses, uncovering the true underlying distributions is complicated by a highly convoluted inverse problem. The determination of PDFs can be understood as the inference of a function supported on $[0,1]$, a problem that admits multiple acceptable solutions. An ensemble of solutions exists that pass all standard goodness-of-fit criteria. In this paper, we propose algorithms for the classification, clustering, and selection of solutions to the determination of PDFs, or any functions on $[0,1]$, based on the characterization of their shape. We explore information-theoretic based (Rényi entropy and divergence) and optimal-transport based (Wasserstein distance) criteria. In particular, we advocate for the use of the Rényi entropy as an {\it absolute} estimator per solution, as opposed to {\it relative} estimators that compare solutions pairwise. We show that the Rényi entropy can characterize the space of solutions {\it w.r.t.} the PDF shapes. Paired with the identification of the optimal combination of solutions via Pareto fronts, it provides a plausible and minimalist selection algorithm. Moreover, Rényi entropy proves versatile for use in clustering applications.

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arXiv2025

Fantômas Unconfined: global QCD fits with Bézier parameterizations

Fantômas is a C++ toolkit for exploring the parametrization dependence of parton distribution functions (PDFs) and other correlator functions in quantum chromodynamics (QCD). Fantômas facilitates the generation of adaptable polynomial parametrizations for PDFs, called metamorphs, to find best-fit PDF solutions and quantify the epistemic uncertainty associated with the parametrizations during their fitting. The method employs Bézier curves as universal approximators for a variety of PDF shapes. Integrated into the xFitter framework for the global QCD analysis, Fantômas provides a foundation for general models of PDFs, while reducing the computational time compared to the approaches utilizing traditional polynomial parametrizations as well as providing an interpretable alternative to neural-network-based models. This paper outlines the structure and practical usage of the Fantômas toolkit, including its inputs, outputs, and implementation within xFitter. It also provides a practical example of using Fantômas for uncertainty quantification as well as the combination of PDF fits into a single ensemble.

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arXiv2025

Fantômas: epistemic and nuclear uncertainties for the parton distributions of the pion

We present Fanto10, a new ensemble of NLO error parton distribution functions (PDFs) in a charged pion that provides the most detailed estimate of uncertainties from experimental, theoretical, and methodological sources in order to enable faithful comparisons against upcoming precision experiments and ab initio QCD predictions. For the first time, the Fanto10 PDFs quantify two important types of uncertainties, arising from in-depth exploration of feasible functional forms of pion PDFs and from the nuclear PDFs describing the internal composition of the tungsten target in the key E615 data set for pion-nuclear Drell-Yan process. Accounting for these uncertainties modifies physics conclusions of more restrictive analyses about the pion's gluon and quark sea composition. These advancements are made by employing the recently developed C++ framework Fantômas for systematic exploration of epistemic sources of PDF uncertainties, such as those arising from the choice of the PDF functional forms and sampling over methodological choices and third-party inputs, e.g., the nuclear PDF uncertainty in the presented case. The framework employs polynomial universal approximators (Bézier curves) to parametrize diverse PDF functional forms and reduce biases associated with the PDF parametrization choice. Its other component combines PDF ensembles from multiple preliminary fits into a single published ensemble of Hessian error PDFs. We review key steps of the Fantômas methodology, properties of Fanto10 PDFs, and implications for future studies.

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arXiv2024

Parametrization sampling and the pion PDF in a phenomenological analysis

In these proceedings, we extend the discussion of the pion PDF obtained by NLO QCD analysis in the Fantômas4QCD framework. Our pion analysis uses a state-of-the-art statistical methodology that accounts for the epistemic uncertainty. Fantômas4QCD, designed to handle multiple functional forms for solving the inverse problem, systematically explores a variety of solutions for PDFs, thereby improving estimates of epistemic uncertainty. Through this novel approach, we interpret our results for the valence sector, considering various non-perturbative methods available for predicting the pion PDF. We emphasize the distinctions between (global) QCD analyses and QFT-based calculations.

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arXiv2024

Fantômas4QCD: pion PDFs with epistemic uncertainties

In these proceedings, we reiterate and extend the discussion of the Next-to-Leading Order (NLO) QCD analysis of the charged pion Parton Distribution Function (PDF) obtained within the Fantômas4QCD framework. The goal of the Fantômas analysis is to quantify the dependence on the parametrization form in global QCD analyses, with a first application to the pion PDFs. We highlight the anti-correlation between the experimentally allowed gluon and sea distributions in the pion, as made apparent by the sampling over parametrization forms. This result, for the sea and gluon sector, illustrates the importance of accounting for epistemic uncertainties in data-driven QCD analyses. In that regard, we further discuss the meaning of the sampling uncertainty and why it is key in phenomenological studies of hadron structure.

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arXiv2024

An analysis of parton distributions in a pion with Bézier parametrizations

We explore the role of parametrizations for nonperturbative QCD functions in global analyses, with a specific application to extending a phenomenological analysis of the parton distribution functions (PDFs) in the charged pion realized in the xFitter fitting framework. The parametrization dependence of PDFs in our pion fits substantially enlarges the uncertainties from the experimental sources estimated in the previous analyses. We systematically explore the parametrization dependence by employing a novel technique to automate generation of polynomial parametrizations for PDFs that makes use of Bézier curves. This technique is implemented in a C++ module Fantômas that is included in the xFitter program. Our analysis reveals that the sea and gluon distributions in the pion are not well disentangled, even when considering measurements in leading-neutron deep inelastic scattering. For example, the pion PDF solutions with a vanishing gluon and large quark sea are still experimentally allowed, which elevates the importance of ongoing lattice and nonperturbative QCD calculations, together with the planned pion scattering experiments, for conclusive studies of the pion structure.

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arXiv2023

Fantômas For QCD: parton distributions in a pion with Bézier parametrizations

We report on a new framework to parametrize parton distribution functions (PDFs) and other hadronic nonperturbative functions using polynomial functions realized by Bézier curves. Bézier parameterizations produce a stable fit with a low number of free parameters, while competing in performance with neural networks and offering explicit interpretation. We specifically apply this approach to determine PDFs in a pion, essential for understanding of nonperturbative QCD dynamics.

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arXiv2023

Quantifying the interplay of experimental constraints in analyses of parton distributions

Parton distribution functions (PDFs) play a central role in calculations for the Large Hadron Collider (LHC). To gain a deeper understanding of the emergence and interplay of constraints on the PDFs in the global QCD analyses, it is important to examine the relative significance and mutual compatibility of the experimental data sets included in the PDF fits. Toward this goal, we discuss the L2 sensitivity, a convenient statistical indicator for exploring the statistical pulls of individual data sets on the best-fit PDFs and identifying tensions between competing data sets. Unlike the Lagrange Multiplier method, the L2 sensitivity can be quickly computed for a range of PDFs and momentum fractions using the published Hessian error sets. We employ the L2 sensitivity as a common metric to study the relative importance of data sets in the recent ATLAS, CTEQ-TEA, MSHT, and reduced PDF4LHC21 PDF analyses at NNLO and approximate N3LO. We illustrate how this method can aid the users of PDFs to identify data sets that are important for a PDF at a given kinematic point, to study quark flavor composition and other detailed features of the PDFs, and to compare the data pulls on the PDFs for various perturbative orders and functional forms. We also address the feasibility of computing the sensitivities using Monte Carlo error PDFs. Together with the article, we present a companion interactive website with a large collection of plotted L2 sensitivities for eight recent PDF releases.

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arXiv2023

The case for an EIC Theory Alliance: Theoretical Challenges of the EIC

We outline the physics opportunities provided by the Electron Ion Collider (EIC). These include the study of the parton structure of the nucleon and nuclei, the onset of gluon saturation, the production of jets and heavy flavor, hadron spectroscopy and tests of fundamental symmetries. We review the present status and future challenges in EIC theory that have to be addressed in order to realize this ambitious and impactful physics program, including how to engage a diverse and inclusive workforce. In order to address these many-fold challenges, we propose a coordinated effort involving theory groups with differing expertise is needed. We discuss the scientific goals and scope of such an EIC Theory Alliance.

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arXiv2023

Parton distributions need representative sampling

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 large-scale population surveys and quasi-Monte Carlo integration methods. In particular, PDF fits may be affected by the big data paradox, which stipulates that more experimental data do not automatically raise the accuracy of PDFs -- close attention to the data quality and sampling of possible PDF solutions is as essential. To test if the sampling of the PDF uncertainty of an experimental observable is truly representative of all acceptable solutions, we introduce a technique (``a hopscotch scan'') based on a combination of parameter scans and stochastic sampling. With this technique, we show that the PDF uncertainty on key LHC cross sections at 13 TeV obtained with the public NNPDF4.0 fitting code is larger than the nominal uncertainty obtained with the published NNPDF4.0 Monte-Carlo replica sets, when accounting for the likelihood distribution. On the same grounds, the uncertainties on the charm distribution at a large momentum fraction $x$ and gluon PDF at small $x$ are enlarged. In PDF ensembles obtained in the analytic minimization (Hessian) formalism, the tolerance on the PDF uncertainty must be based on sufficiently complete sampling of PDF functional forms and choices of the experiments.

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arXiv2022

Extraction of the higher-twist parton distribution $e(x)$ from CLAS data

This manuscript presents the new analysis of recent CLAS and CLAS12 data aimed at the extraction of $e(x)$. This publication benefits from a proof-of-principle analysis of a smaller preliminary data set published in a preprint form in \url{1405.7659}. We present the first point-by-point extraction of a twist-3 PDF. The scalar PDF, $e(x)$, is accessed through the analysis of the data for the $\sinϕ_R$-moment of the beam-spin asymmetry for dihadron production in semi-inclusive DIS off proton target at CLAS and CLAS12. The dihadron formalism allows for use of collinear framework, hence calling for a minimal set of approximations and hypotheses. The extracted PDF $e(x)$ carries insights into the physics of the largely-unexplored quark-gluon correlations, and its first Mellin moment is related to the marginally-known scalar charge of the nucleon. We show that the proton flavor combination of the scalar PDF is non-zero at more than $74\%$ probability.

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arXiv2022

The PDF4LHC21 combination of global PDF fits for the LHC Run III

A precise knowledge of the quark and gluon structure of the proton, encoded by the parton distribution functions (PDFs), is of paramount importance for the interpretation of high-energy processes at present and future lepton-hadron and hadron-hadron colliders. Motivated by recent progress in the PDF determinations carried out by the CT, MSHT, and NNPDF groups, we present an updated combination of global PDF fits: PDF4LHC21. It is based on the Monte Carlo combination of the CT18, MSHT20, and NNPDF3.1 sets followed by either its Hessian reduction or its replica compression. Extensive benchmark studies are carried out in order to disentangle the origin of the differences between the three global PDF sets. In particular, dedicated fits based on almost identical theory settings and input datasets are performed by the three groups, highlighting the role played by the respective fitting methodologies. We compare the new PDF4LHC21 combination with its predecessor, PDF4LHC15, demonstrating their good overall consistency and a modest reduction of PDF uncertainties for key LHC processes such as electroweak gauge boson production and Higgs boson production in gluon fusion. We study the phenomenological implications of PDF4LHC21 for a representative selection of inclusive, fiducial, and differential cross sections at the LHC. The PDF4LHC21 combination is made available via the LHAPDF library and provides a robust, user-friendly, and efficient method to estimate the PDF uncertainties associated to theoretical calculations for the upcoming Run III of the LHC and beyond.

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arXiv2022

NNLO constraints on proton PDFs from the SeaQuest and STAR experiments and other developments in the CTEQ-TEA global analysis

We review progress in the global QCD analysis by the CTEQ-TEA group since the publication of CT18 parton distribution functions (PDFs) in the proton. Specifically, we discuss comparisons of CT18 NNLO predictions with the LHC 13 TeV measurements as well as with the FNAL SeaQuest and BNL STAR data on lepton pair production. The specialized CT18X PDFs approximating saturation effects are compared with the CT18sx PDFs obtained using NLL/NLO small-$x$ resummation. Short summaries are presented for the special CT18 parton distributions with fitted charm and with lattice QCD inputs. A recent comparative analysis of the impact of deuteron nuclear effects on the parton distributions by the CTEQ-JLab and CTEQ-TEA groups is summarized.

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arXiv2021

Large-x power laws of parton distributions remain inconclusive

Focusing on hadron scattering at large partonic momentum fractions $x$, we compare nonperturbative QCD predictions for the asymptotic behavior of DIS structure functions and parton distribution functions (PDFs) to the $x$ and $Q$ dependence of phenomenological PDFs. In the CT18 NNLO global QCD analysis, higher-order radiative contributions and functional mimicry of PDF parametrizations result in about one unit of uncertainty in the effective powers of $(1-x)$ falloff of nucleon PDFs. Similar uncertainties are present in the case of the pion PDF, an object of growing interest in phenomenology.

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arXiv2021

Nucleon and pion PDFs: large-x asymptotics meets functional mimicry

We review strategies to unveil the primordial large-$x$ structure of the nucleons as well as the pion from hard-scattering experiments. Ideas are presented for learning about the $x\to 1$ limit of nonperturbative QCD dynamics at energy scales of order 1 GeV from collider experiments at much higher scales. The behavior of parton distributions at $x\to 1$ predicted by the quark counting rules and other low-energy theoretical approaches is contrasted with phenomenological PDFs. Polynomial mimicry of PDF parametrizations is one of many factors that influence the apparent power of the $(1-x)$ falloff. We discuss implications of the mimicry for the large-$x$ falloff of the pion PDFs.

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arXiv2020

Parton distributions and lattice QCD calculations: toward 3D structure

The strong force which binds hadrons is described by the theory of Quantum Chromodynamics (QCD). Determining the character and manifestations of QCD is one of the most important and challenging outstanding issues necessary for a comprehensive understanding of the structure of hadrons. Within the context of the QCD parton picture, the Parton Distribution Functions (PDFs) have been remarkably successful in describing a wide variety of processes. However, these PDFs have generally been confined to the description of collinear partons within the hadron. New experiments and facilities provide the opportunity to additionally explore the transverse structure of hadrons which is described by Generalized Parton Distributions (GPDs) and Transverse Momentum Dependent Parton Distribution Functions (TMD PDFs). In our previous review, we compared and contrasted the two main approaches used to determine the collinear PDFs: the first based on perturbative QCD factorization theorems, and the second based on lattice QCD calculations. In the present report, we provide an update of recent progress on the collinear PDFs, and also expand the scope to encompass the generalized PDFs (GPDs and TMD PDFs). We review the current state of the various calculations, and consider what new data might be available in the near future. We also examine how a shared effort can foster dialog between the PDF and Lattice QCD communities, and yield improvements for these generalized PDFs.

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arXiv2020

Probing Nucleons and Nuclei in High Energy Collisions

This volume is a collection of contributions for the 7-week program "Probing Nucleons and Nuclei in High Energy Collisions" that was held at the Institute for Nuclear Theory in Seattle, WA, USA, from October 1 until November 16, 2018. The program was dedicated to the physics of the Electron Ion Collider (EIC), the world's first polarized electron-nucleon (ep) and electron-nucleus (eA) collider to be constructed in the USA. These proceedings are organized by chapters, corresponding to the weeks of the program: Week I, Generalized parton distributions; Week II, Transverse spin and TMDs; Week III, Longitudinal spin; Week IV, Symposium week; Weeks V & VI, eA collisions; Week VII, pA and AA collisions. We hope these proceedings will be useful to readers as a compilation of EIC-related science at the end of the second decade of the XXI century.

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