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Pavel Nadolsky

Publications and source records attributed to Pavel Nadolsky.

At least 19 recordsLinked to original sources
arXiv2026

CT25: the new generation of CTEQ-TEA PDFs

This contribution reviews CT25, a new generation of CTEQ--TEA parton distribution functions (PDFs) for precision QCD. With its first member sets released in 2025, the CT25 family addresses common uses of parton distributions in diverse contexts. We describe the CTEQ--TEA Parton Cloud, an online database of exploratory global fits to precision QCD measurements, from which we select PDF solutions for general- and special-purpose calculations. These solutions are published as complementary error PDF ensembles---the baseline CT25, CT25m, CT25pd, and ensembles with conservative priors---optimized for distinct uses. They implement new approaches to quantifying uncertainties and different treatments of theoretical, parametrization, and nuclear-target uncertainties. In particular, they provide complementary frameworks for exploring PDF uncertainties at large partonic momentum fractions relevant to HL-LHC and EIC studies. Further details will appear in the forthcoming CT25 publication.

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arXiv2026

Toward N$^3$LO CT global PDF analyses: The SACOT-$χ$ scheme in DIS and DGLAP evolution at partial N$^3$LO

We discuss three aspects of the ongoing efforts of the CTEQ--TEA group toward global parton distribution function (PDF) analyses beyond NNLO accuracy in QCD. First, we present a realization of the SACOT-$χ$ general-mass variable flavor number scheme for deep-inelastic scattering (DIS) at the partial next-to-next-to-next-to-leading order (pN$^3$LO) in QCD. We numerically illustrate how this SACOT-$χ$ theory prediction captures the dependence of DIS structure functions on masses of heavy quarks with inclusion of the available $O(α_s^3)$ contributions. Second, we discuss a preliminary pN$^3$LO CT25 fit that implements such contributions. Third, we extend the Candia algorithm for solving DGLAP evolution equations for unpolarized parton distribution functions (PDFs) in $x$ space to N$^3$LO in QCD. The algorithm is based on logarithmic expansions of the solution and can be extended to all orders in QCD. An expansion equivalent to the exact DGLAP solution at N$^3$LO is presented in the non-singlet sector. We show results for approximate N$^3$LO PDFs evolved using the most recent approximations to the 4-loop splitting functions in QCD.

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arXiv2026

Strong Coupling Constant Determination from the new CTEQ-TEA Global QCD Analysis

We present a new determination of the strong coupling constant $α_s$ from a global QCD analysis CT25 of parton distribution functions (PDFs) that incorporates high-precision experimental measurements from the Run-2 of the Large Hadron Collider together with a large sample of other measurements over a wide interval of energies. This work addresses two objectives: providing an up-to-date determination of $α_s$ using NNLO calculations and a sensitive nucleon data set within a self-consistent framework, and critically assessing the robustness of the $α_s(M_Z)$ extraction in light of systematic uncertainties as well as correlations of $α_s(M_Z)$ with the functional forms of PDFs and other model parameters. In regard to the uncertainty assessment, we demonstrate that some commonly used criteria, including the dynamical tolerance and Bayesian hierarchical models, may produce significantly different or even unstable estimates for the net $α_s$ uncertainty, and we introduce a concept of \textit{data-clustering safety} that the replicable uncertainty estimates must satisfy. Based on this in-depth examination of the CT25 global hadronic data set using a combination of analysis methods, and after demonstrating a weak correlation between $α_s$ and the functional forms of CT25 PDF parametrizations, we find $α_s(M_Z)=0.1183^{+0.0023}_{-0.0020}$ at the 68\% credibility level.

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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

QED-enhanced PDF implications for the Higgs sector

In this work, we examine the implications of electroweak corrections beyond leading order for processes of special interest in the Higgs sector. We especially explore the role of these corrections given the introduction of an explicit parton distribution function (PDF) for the photon in the proton, an object which emerges necessarily in global PDF fits which include QED effects (i.e., QED-enhanced PDFs). We concentrate on several representative cases, including total Higgs-production cross sections through gluon fusion, $gg \to H$, vector-boson fusion (VBFH), and associated production, $pp \to VH$; we also examine differential distributions, taking a representative Higgs-strahlung process, $pp \to W^+H$. We find that the recently developed LUX formalism for the photon PDF significantly stabilizes the PDF dependence of both QED-PDF and electroweak corrections in the Higgs sector, while leaving overall $\sim\!3\!-\!4\%$ cross-section-level variations, depending on the chosen QED-enhanced PDF. We illustrate this QED-enhanced PDF dependence by exploring predictions based upon recent analyses of the CTEQ-TEA, MSHT, and NNPDF analysis groups, fitted either at NNLO or approximate N3LO in QCD.

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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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arXiv2025

GRB Redshift Classifier to Follow-up High-Redshift GRBs Using Supervised Machine Learning

Gamma-ray bursts (GRBs) are intense, short-lived bursts of gamma-ray radiation observed up to a high redshift ($z \sim 10$) due to their luminosities. Thus, they can serve as cosmological tools to probe the early Universe. However, we need a large sample of high$-z$ GRBs, currently limited due to the difficulty in securing time at the large aperture Telescopes. Thus, it is painstaking to determine quickly whether a GRB is high$z$ or low$-z$, which hampers the possibility of performing rapid follow-up observations. Previous efforts to distinguish between high$-$ and low$-z$ GRBs using GRB properties and machine learning (ML) have resulted in limited sensitivity. In this study, we aim to improve this classification by employing an ensemble ML method on 251 GRBs with measured redshifts and plateaus observed by the Neil Gehrels Swift Observatory. Incorporating the plateau phase with the prompt emission, we have employed an ensemble of classification methods to enhance the sensitivity unprecedentedly. Additionally, we investigate the effectiveness of various classification methods using different redshift thresholds, $z_{threshold}$=$z_t$ at $z_{t}=$ 2.0, 2.5, 3.0, and 3.5. We achieve a sensitivity of 87\% and 89\% with a balanced sampling for both $z_{t}=3.0$ and $z_{t}=3.5$, respectively, representing a 9\% and 11\% increase in the sensitivity over Random Forest used alone. Overall, the best results are at $z_{t} = 3.5$, where the difference between the sensitivity of the training set and the test set is the smallest. This enhancement of the proposed method paves the way for new and intriguing follow-up observations of high$-z$ GRBs.

astro-ph.HE↗
arXiv2025

General mass variable flavor number scheme for $Z$ boson production in association with a heavy quark at hadron colliders

We present a methodology to streamline implementation of massive-quark radiative contributions in calculations with a variable number of active partons in proton-proton collisions. The methodology introduces \textit{subtraction} and \textit{residual} heavy-quark parton distribution functions (PDFs) to implement calculations in the Aivazis-Collins-Olness-Tung (ACOT) factorization scheme and its simplified realization in various processes up to the next-to-the-next-to-leading order in the QCD coupling strength. Interpolation tables for bottom-quark subtraction and residual distributions for CT18 NLO and NNLO PDF ensembles are provided in the common LHAPDF6 format. A numerical calculation of $Z$-boson production with at least one $b$ jet at the Large Hadron Collider beyond the lowest order in QCD is considered for illustration purposes.

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arXiv2024

The impact of LHC precision measurements of inclusive jet and dijet production on the CTEQ-TEA global PDF fit

In this study, we investigate the impact of new LHC inclusive jet and dijet measurements on parton distribution functions (PDFs) that describe the proton structure, with a particular focus on the gluon distribution at large momentum fraction, $x$, and the corresponding partonic luminosities. We assess constraints from these datasets using next-to-next-to-leading-order (NNLO) theoretical predictions, accounting for a range of uncertainties from scale dependence and numerical integration. From the scale choices available for the calculations, our analysis shows that the central predictions for inclusive jet production show a smaller scale dependence than dijet production. We examine the relative constraints on the gluon distribution provided by the inclusive jet and dijet distributions and also explore the phenomenological implications for inclusive $H$, $t\bar{t}$, and $t\bar{t}H$ production at the LHC at 14 TeV.

hep-ph↗
arXiv2024

General Mass treatment for Z boson production in association with a heavy quark at hadron colliders

We present the application of the ACOT and S-ACOT general mass variable flavor number schemes to proton-proton collisions with particular attention to the production of final states with at least one heavy quark. Subtraction and residual heavy-quark parton distribution functions are introduced to facilitate the implementation of this scheme at higher orders in perturbative QCD. The calculation of Z-boson hadronic production with at least one $b$ jet beyond the lowest order in QCD is considered for illustration purposes.

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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.

hep-ph↗
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.

hep-ph↗
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 persistent nonperturbative charm enigma

The question of the existence and possible magnitude of nonperturbative (often called "intrinsic") charm in the proton has long confounded attempts to cleanly isolate such a contribution in global analyses of high-energy experiments. In this letter, we show that the available (non)perturbative QCD theory and hadronic data have still not developed to a sufficient level to clearly resolve this problem. We highlight a number of challenging aspects that must be confronted in extracting nonperturbative charm in PDF fits, and in so doing, present an updated next-to-next-to-leading order CT analysis of fitted charm, CT18 FC, which we also compare to recent studies. We outline the theory developments and future data needed to make progress on this subject.

hep-ph↗
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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