arXiv subjects

Felix Hekhorn

Publications and source records attributed to Felix Hekhorn.

At least 19 recordsLinked to original sources

arXiv2026

New parton distribution functions of the real photon

Precise determination of the partonic structure of real photons has attracted renewed interest in view of ongoing studies of high-energy photon-induced processes in ultraperipheral collisions (UPCs) at the Large Hadron Collider (LHC) and the future Electron-Ion Collider (EIC). Despite being fundamental in their own right and essential for QCD phenomenology of hard processes initiated by resolved photons, the quark and gluon distributions of the photon are poorly known and merit a new analysis employing modern tools of statistical data analysis. We determine new sets of leading-order (LO) and next-to-leading-order (NLO) parton distributions (PDFs) for the real photon, dubbed VALO1.0, by performing a global QCD analysis of the world data on the photon structure function $F_2^γ$ measured in deep-inelastic scattering (DIS) processes on a real photon target in electron-positron collisions. Our analysis improves on the results available in the literature by providing uncertainties in the form of Monte Carlo replicas and the photon PDFs in the LHAPDF6 format. We observe that while the electron-positron data allow us to determine the singlet quark distribution very well at both LO and NLO, the gluon distribution is constrained to a much lesser degree, especially at LO. For this analysis, we have developed an open-source framework, which extends the pineline framework, developed for the proton, to the photon case and includes the program solving the inhomogeneous scale evolution of photon PDFs, $γ$EKO.

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arXiv2026

Towards the new NNPDF4.1 global analysis

We review progress and plans towards a new global PDF analysis from the NNPDF Collaboration. This new release will be based on state-of-the-art theory calculations, and in particular will be based on exact NNLO interpolation grids, (approximate) N3LO QCD corrections to DGLAP evolution and DIS structure functions, and QED effects to DGLAP evolution. All relevant sources of experimental and theoretical uncertainties, the latter including missing higher orders and higher twists, are taken into account. As compared to NNPDF4.0, this new release includes more than 25 new datasets from HERA jets to Drell-Yan (inclusive and with extra jets), top quark, and jet production at the LHC among others. Our machine learning methodology is statistically validated by extensive closure and future tests and benefits from an improved hyperoptimization algorithm.

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arXiv2026

Towards new D meson fragmentation functions

The Heavy Meson (Hymn) collaboration presents a new extraction of D meson fragmentation functions using experimental data from LEP and LHC. We focus particularly on kinematical regimes where perturbative QCD should be safely applicable to avoid contamination from higher-twist effects which could lead to an apparent process dependence of fragmentation functions. We account for the initial-state radiation and, as a novel ingredient, consider the prompt and non-prompt contributions separately. The analysis is carried out at next-to-leading order accuracy including uncertainty estimation based on Monte-Carlo replica technique. We disucss the exemplary case of $\mathrm{D}^0$ here and defer the results for $\mathrm{D}^\pm$ and $\mathrm{D}^{*,\pm}$ to a forthcoming publication.

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arXiv2026

Deeply Inelastic Scattering Revisited

Due to its conceptual simplicity, Deeply Inelastic Scattering (DIS) often serves as a textbook example for Quantum Chromo Dynamics (QCD) and partonic structure of nucleons. However, it is this supposed simplicity, which makes DIS an ideal case for discussing many additional effects and corrections. In these lectures we discuss DIS within the domain of perturbative QCD covering a range of topics ranging from mathematical problems to kinematical corrections, and to practical challenges when attempting to interpret experimental measurements. Although here we focus on the exemplary case of DIS, the discussed topcis are relevant to a larger class of processes. We also give an overview of existing and future DIS measurements, and discuss their implementation into modern extractions of parton distribution functions (PDFs) which quantify the partonic structure of nucleons. The discussed features are all implemented in the open source code Yadism, which has been used for PDF extractions from a wide range of the available world data on fully inclusive DIS.

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arXiv2026

VALO1.0: New real-photon parton distributions with Monte Carlo uncertainties

Performing a global QCD analysis of data on the photon structure function $F_2^γ$ in $e^{+} e^{-}$ scattering, we determine new leading order (LO) and next-to-leading (NLO) parton distributions functions (PDFs) of the real photon. The resulting photon PDFs, referred to as VALO1.0, are obtained in the form of Monte Carlo (MC) replicas which assess the propagation of experimental uncertainties to the PDFs. To achieve well-converging fits, we employ a five-parameter hadron-like ansatz for the boundary conditions with simplifying assumptions on the flavor structure of the quark distributions and the large-$x$ behavior of the gluon distribution. This results in robust quark distributions at both LO and NLO and the gluon distribution at NLO with modest uncertainties, while leaving LO gluons still largely unconstrained. The resulting photon PDFs broadly agree with the parameterizations available in the literature and set the stage for future analyses including additional photoproduction data, which could help to increase the flexibility of our input PDFs. The LO and NLO VALO1.0 photon-PDF replicas, both in the DIS$_γ$ and $\overline{\rm MS}$ factorization schemes as well as the open-source $γ\texttt{EKO}$ code for solving the scale dependence of photon PDFs and the analysis framework $\texttt{VALOfitter}$ are made publicly available.

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arXiv2026

Inclusive charm and bottom quark pair production cross sections at hadron colliders at next-to-next-to-leading-order accuracy

The inclusive cross sections for charm ($\mathrm{c}\overline{\mathrm{c}}$) and bottom ($\mathrm{b}\overline{\mathrm{b}}$) quark-antiquark pair production in proton-proton, proton-antiproton, and proton-nucleus collisions are studied over a wide range of center-of-mass energies, $\sqrt{s}\approx 10$ GeV--400 TeV. All existing data over $\sqrt{s}\approx 10$ GeV--14 TeV are collected and compared to calculations at next-to-next-to-leading-order (NNLO) accuracy using the new fixed-order MaunaKea open-source code for varying sets of parton distribution functions (PDFs). Relative to next-to-leading-order (NLO) predictions, the NNLO cross sections are enhanced by up to a factor of two, with the associated theoretical scale uncertainties reduced by the same amount, leading to agreement with experimental data over the full range of collision energies. The NNLO results are also compared with NLO predictions obtained within the SACOT-$m_{_\mathrm{T}}$ general-mass variable-flavour-number scheme. Despite still sizable theoretical and experimental uncertainties, $\mathrm{c}\overline{\mathrm{c}}$ cross section at multi-TeV energies can provide extra constraints on the gluon density at very small-$x$ in global PDF analyses. In the bottom sector, more precise cross section measurements at low energies, $\sqrt{s}\approx 10$--100 GeV, can help constraint the bottom-quark pole mass.

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arXiv2026

On the positivity of MSbar parton distributions

We revisit our argument that shows that parton distribution Functions (PDFs) in the MSbar{ scheme are non-negative in the perturbative region, with the main goals of elucidating its domain of validity and clarifying its theoretical underpinnings. We specifically discuss recent results proving that PDFs can turn negative at sufficiently low scale, we clarify quantitatively various aspects of our derivation of positivity in the perturbative region, and we provide an estimate for the scale above which PDF positivity holds.

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arXiv2026

Parton distribution functions and theory parameters: an NNPDF perspective

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.

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arXiv2025

A Determination of $α_s(m_Z)$ at ${\bf aN^3LO_{QCD}}\otimes {\bf {NLO}_{QED}}$ Accuracy from a Global PDF Analysis

We present a determination of the strong coupling $α_s(m_Z)$ from a global dataset including both fixed-target and collider data from deep-inelastic scattering and a variety of hadronic processes, with a simultaneous determination of parton distribution functions (PDFs) based on the NNPDF4.0 methodology. This determination is performed at NNLO and approximate N$^3$LO (aN$^3$LO) perturbative QCD accuracy, including QED corrections and a photon PDF up to NLO accuracy. We extract $α_s$ using two independent methodologies, both of which take into account the cross-correlation between $α_s$ and the PDFs. The two methodologies are validated by closure tests that allow us to detect and remove or correct for several sources of bias, and lead to mutually consistent results. We account for all correlated experimental uncertainties, as well as correlated theoretical uncertainties related to missing higher order perturbative corrections (MHOUs). We study the perturbative convergence of our results and the impact of QED corrections. We assess individual sources of uncertainty, specifically MHOUs and the value of the top quark mass. We provide a detailed appraisal of methodological choices, including the choice of input dataset, the form of solution of evolution equation, the treatment of the experimental covariance matrix, and the details of Monte Carlo data generation. We find $α_s(m_Z)=0.1194^{+0.0007}_{-0.0014}$ at aN$^3$LO$_{\rm QCD}\otimes {\rm NLO}_{\rm QED}$ accuracy, consistent with the latest PDG average and with recent lattice results.

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arXiv2025

Combination of aN$^3$LO PDFs and implications for Higgs production cross-sections at the LHC

We discuss how the two existing approximate N$^3$LO (aN$^3$LO) sets of parton distributions (PDFs) from the MSHT20 and NNPDF4.0 series can be combined for LHC phenomenology, both in the pure QCD case and for the QCD$\otimes$QED sets that include the photon PDF. Using the resulting combinations, we present predictions for the total inclusive cross-section for Higgs production in gluon fusion, vector boson fusion, and associated production at the LHC Run-3. For the gluon fusion and vector boson fusion channels, the corrections that arise when using correctly matched aN$^3$LO PDFs with N$^3$LO cross section calculations, compared to using NNLO PDFs, are significant, in many cases larger than the PDF uncertainty, and generally larger than the differences between the two aN$^3$LO PDF sets entering the combination. The combined aN$^3$LO PDF sets, MSHT20xNNPDF40_an3lo and MSHT20xNNPDF40_an3lo_qed, are made publicly available in the LHAPDF format and can be readily used for LHC phenomenology.

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arXiv2025

NNPDFpol2.0: a global determination of polarised PDFs and their uncertainties at next-to-next-to-leading order

We present NNPDFpol2.0, a new set of collinear helicity parton distribution functions (PDFs) of the proton based on legacy measurements of structure functions in inclusive neutral-current longitudinally polarised deep-inelastic scattering (DIS), and of W -boson, single-inclusive, and di-jet production asymmetries in longitudinally polarised proton-proton collisions. The determination is accurate to next-to-next-to-leading order in the strong coupling, and includes heavy quark mass corrections in the analysis of DIS data. Uncertainties due to missing higher-order corrections are systematically incorporated by means of a covariance matrix determined by scale variations. NNPDFpol2.0 is based on a machine learning methodology, that makes use of Monte Carlo sampling for the representation of uncertainties into PDFs, of a neural network for the parametrisation of PDFs, of stochastic gradient descent for the optimisation of PDF parameters, and of hyperoptimisation for the selection of the best fitting model. We study the impact on PDFs of higher-order corrections, of the positivity constraint, and of the data. We demonstrate two phenomenological applications of NNPDFpol2.0, specifically the determination of the proton spin fraction carried by gluons and quarks, and of theoretical predictions for single-hadron production in longitudinally polarised DIS and proton-proton collisions.

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arXiv2025

Towards N$^3$LO PDFs and their implications for Higgs production cross-sections

We review the recently published PDF sets MSHT20xNNPDF40_an3lo and MSHT20xNNPDF40_an3lo_qed, which have been obtained by combining the approximate N$^3$LO (aN$^3$LO) sets of parton distributions (PDFs) from the MSHT20 and NNPDF4.0 series. We investigate the impact of the most recent results on N$^3$LO splitting functions onto the two PDF sets. Finally, we demonstrate the impact of N$^3$LO PDFs on the computation of Higgs production cross-sections at the LHC.

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arXiv2024

An FONLL prescription with coexisting flavor number PDFs

We present a new prescription to account for heavy quark mass effects in the determination of parton distribution functions (PDFs) based on the FONLL scheme. Our prescription makes explicit use of the freedom to choose the number of active flavors at a given scale and, thus, use coexisting PDFs with different active flavor number. This new prescription is perturbatively equivalent to the former but improves the implementation in two ways. First, it can be naturally generalized to account simultaneously for multiple heavy quark effects, such as charm and bottom effects, which can both be relevant at the same scale due to the small mass difference. Second, it can be trivially generalized to use at any fixed-order or collinear resummed accuracy, while previous prescriptions required ad-hoc expansions of the DGLAP evolution kernels for each coefficient. We supplement the paper with codes for the computation of deep inelastic scattering observables in this new prescription.

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arXiv2024

Yadism: Yet Another Deep-Inelastic Scattering Module

We present yadism, a library for the evaluation of both polarized and unpolarized deep-inelastic scattering (DIS) structure functions and cross sections up to N$^3$LO in perturbative QCD. The package provides computations of observables in fixed-flavor and zero-mass variable flavor number schemes. The implementation of the general mass variable flavor number schemes is supported through the high virtuality limits for the heavy flavor coefficients. In addition, yadism provides a set of tools for the generation of interpolation grids in the PDF-independent PineAPPL format, allowing to test the PDF dependence on any DIS observable without needing to rerun the computation. This work is part of an ongoing effort to standardize the format of theory predictions in high-energy physics within the pineline framework. The code is open source, written in Python and documented to facilitate usage, integrations, and further extensions. Finally, the code has been benchmarked against the widely used APFEL++ and QCDNUM libraries.

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arXiv2024

The Path to N$^3$LO Parton Distributions

We extend the existing leading (LO), next-to-leading (NLO), and next-to-next-to-leading order (NNLO) NNPDF4.0 sets of parton distribution functions (PDFs) to approximate next-to-next-to-next-to-leading order (aN$^3$LO). We construct an approximation to the N$^3$LO splitting functions that includes all available partial information from both fixed-order computations and from small and large $x$ resummation, and estimate the uncertainty on this approximation by varying the set of basis functions used to construct the approximation. We include known N$^3$LO corrections to deep-inelastic scattering structure functions and extend the FONLL general-mass scheme to $\mathcal{O}\left( α_s^3\right)$ accuracy. We determine a set of aN$^3$LO PDFs by accounting both for the uncertainty on splitting functions due to the incomplete knowledge of N$^3$LO terms, and to the uncertainty related to missing higher corrections (MHOU), estimated by scale variation, through a theory covariance matrix formalism. We assess the perturbative stability of the resulting PDFs, we study the impact of MHOUs on them, and we compare our results to the aN$^3$LO PDFs from the MSHT group. We examine the phenomenological impact of aN$^3$LO corrections on parton luminosities at the LHC, and give a first assessment of the impact of aN$^3$LO PDFs on the Higgs and Drell-Yan total production cross-sections. We find that the aN$^3$LO NNPDF4.0 PDFs are consistent within uncertainties with their NNLO counterparts, that they improve the description of the global dataset and the perturbative convergence of Higgs and Drell-Yan cross-sections, and that MHOUs on PDFs decrease substantially with the increase of perturbative order.

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arXiv2024

Photons in the proton: implications for the LHC

We construct a set of parton distribution functions (PDFs), based on the recent NNPDF4.0 PDF set, that also include a photon PDF. The photon PDF is constructed using the LuxQED formalism, while QED evolution accounting for O(alpha), O(alpha alphas) and O(alpha^2) corrections is implemented and benchmarked by means of the EKO code. We investigate the impact of QED effects on NNPDF4.0, and compare our results both to our previous NNPDF3.1QED PDF set and to other recent PDF sets that include the photon. We assess the impact of photon-initiated processes and electroweak corrections on a variety of representative LHC processes, and find that they can reach the 5% level in vector boson pair production at large invariant mass.

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arXiv2024

Determination of the theory uncertainties from missing higher orders on NNLO parton distributions with percent accuracy

We include uncertainties due to missing higher order corrections to QCD computations (MHOU) used in the determination of parton distributions (PDFs) in the recent NNPDF4.0 set of PDFs. We use our previously published methodology, based on the treatment of MHOUs and their full correlations through a theory covariance matrix determined by scale variation, now fully incorporated in the new NNPDF theory pipeline. We assess the impact of the inclusion of MHOUs on the NNPDF4.0 central values and uncertainties, and specifically show that they lead to improved consistency of the PDF determination with an ensuing moderate reduction of PDF uncertainties at NNLO.

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arXiv2024

Towards NNPDFpol2.0

We review the recent efforts in the NNPDF Collaboration towards a new global extraction of polarized parton distributions functions (pPDF). Polarized PDFs are highly relevant for the interpretation of current and future polarized high-energy experiments, including the upcoming Electron-Ion Collider (EIC). We present a recent study of the role played by heavy quark effects in polarized DIS, where we apply the FONLL general-mass variable-flavour-number scheme for the first time in a polarized setup and demonstrate the significant impact of charm mass corrections, specifically for the polarized gluon distribution. We show preliminary results (DIS-only) of this new pPDF release, NNPDFpol2.0, based on the NNPDF4.0 fitting machinery and the associated new theory prediction pipeline.

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