We present , an interpolation library that supports both collinear and transverse momentum-dependent parton distribution functions. is designed to be fast and reliable, with modern functionalities that target both current and future hadron collider experiments. It aims to address the shortcomings of existing interpolation libraries while providing additional features to support generic non-perturbative functions. Some of the features include a new interpolation based on Chebyshev polynomials, as well as the ability to interpolate along the nucleon number $ extit{A}$, the reference strong coupling $$alpha _s(M_Z)$$ , and the parton’s intrinsic transverse momentum $$k_T$$ . implements its own file format using binary serialisation and lossless compression, prioritising speed and efficiency. A no-code migration design is provided for in order to remove the friction associated with transitioning to . The library is written in Rust, with interfaces for various programming languages such as Fortran, C, C++, Python, and Mathematica. We benchmark against and for various sets and show that it is both fast and accurate.

Netherlands

Tanjona Rabemananjara

NeoPDF: a fast interpolation library for collinear and transverse momentum-dependent parton distributions

We present NNPDF 2.0, 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 $\textit{W}$ -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. NNPDF 2.0 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 NNPDF 2.0, 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.

Switzerland

Juan Cruz-Martinez

Toon Hasenack

Finland

Felix Hekhorn

Giacomo Magni

Italy

Emanuele Nocera

Juan Rojo

Tanishq Sharma

Gijs Seeventer

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

We present a systematic comparison of theoretical predictions and various high-precision experimental measurements, specifically of differential cross sections performed by the LHC run II for Drell-Yan gauge boson, top-quark pair, single-inclusive jet and di-jet production, and by HERA for single-inclusive jet and di-jet production. Theoretical predictions are computed at next-to-next-to-leading order (NNLO) accuracy in perturbative Quantum Chromodynamics. The most widely employed sets of Parton Distribution Functions (PDFs) are used, and PDF, strong coupling, and missing higher order uncertainties are taken into account. We quantitatively assess the predictive power of each PDF set and the contribution of the different sources of experimental and theoretical uncertainty to the agreement between data and predictions. We show that control over all of these aspects is crucial to precision physics studies, such as the determination of Standard Model parameters at the LHC.

United Kingdom

Amedeo Chiefa

Mark Costantini

Roy Stegeman

Maria Ubiali

Parton distributions confront LHC Run II data: a quantitative appraisal

Proton-proton collisions at energy-frontier facilities produce an intense flux of high-energy light particles, including neutrinos, in the forward direction. At the LHC, these particles are currently being studied with the far-forward experiments FASER/FASER$\textit{ν}$ and SND@LHC, while new dedicated experiments have been proposed in the context of a Forward Physics Facility (FPF) operating at the HL-LHC. Here we present a first quantitative exploration of the reach for neutrino, QCD, and BSM physics of far-forward experiments integrated within the proposed Future Circular Collider (FCC) project as part of its proton-proton collision program (FCC-hh) at $$ \sqrt{s} $$ ≃ 100 TeV. We find that 10 electron/muon neutrinos and 10 tau neutrinos could be detected, an increase of several orders of magnitude compared to (HL-)LHC yields. We study the impact of neutrino DIS measurements at the FPF@FCC to constrain the unpolarised and spin partonic structure of the nucleon and assess their sensitivity to nuclear dynamics down to $\textit{x}$ ∼ 10 with neutrinos produced in proton-lead collisions. We demonstrate that the FPF@FCC could measure the neutrino charge radius for $\textit{ν}$ and $\textit{ν}$ and reach down to five times the SM value for $\textit{ν}$ . We fingerprint the BSM sensitivity of the FPF@FCC for a variety of models, including dark Higgs bosons, relaxion-type scenarios, quirks, and millicharged particles, finding that these experiments would be able to discover LLPs with masses as large as 50 GeV and couplings as small as 10 , and quirks with masses up to 10 TeV. Our study highlights the remarkable opportunities made possible by integrating far-forward experiments into the FCC project, and it provides new motivation for the FPF at the HL-LHC as an essential precedent to optimize the forward physics experiments that will enable the FCC to achieve its full physics potential.

United States

Roshan Mammen Abraham

Poland

Jyotismita Adhikary

Jonathan Feng

Max Fieg

Germany

Felix Kling

China

Jinmian Li

Junle Pei

Sebastian Trojanowski

FPF@FCC: neutrino, QCD, and BSM physics opportunities with far-forward experiments at a 100 TeV Proton Collider

We present NNPDF4.0MC, a variant of the NNPDF4.0 set of parton distributions (PDFs) at LO, NLO and NNLO, with and without inclusion of the photon PDF, suitable for use with Monte Carlo (MC) event generators, which require PDFs to satisfy additional constraints in comparison to standard PDF sets. These requirements include PDF positivity down to a low scale Q ~ 1 GeV, smooth extrapolation in the very small and large x regions, and numerically stable results even in extreme regions of phase space for all PDFs. We compare the NNPDF4.0MC PDFs to their baseline NNPDF4.0 counterparts, and to the NNPDF2.3LO set entering the Monash tune of the Pythia8 event generator. We briefly assess the phenomenological impact of these PDFs on the cross-sections for hard and soft QCD processes at the LHC.

CERN

Stefano Forte

Niccolò Laurenti

LO, NLO, and NNLO parton distributions for LHC event generators

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 $$^{3}$$  <math> <mmultiscripts> <mrow></mrow> <mrow></mrow> <mn>3</mn> </mmultiscripts> </math>  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.

Alessandro Candido

Yadism: yet another deep-inelastic scattering module

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 ( $$\hbox {aN}^3\hbox {LO}$$  <math> <mrow> <msup> <mtext>aN</mtext> <mn>3</mn> </msup> <mtext>LO</mtext> </mrow> </math>  ). We construct an approximation to the  $$\hbox {N}^3\hbox {LO}$$  <math> <mrow> <msup> <mtext>N</mtext> <mn>3</mn> </msup> <mtext>LO</mtext> </mrow> </math>   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  $$\hbox {N}^3\hbox {LO}$$  <math> <mrow> <msup> <mtext>N</mtext> <mn>3</mn> </msup> <mtext>LO</mtext> </mrow> </math>   corrections to deep-inelastic scattering structure functions and extend the FONLL general-mass scheme to  $$\mathcal {O}\left( \alpha _s^3\right) $$  <math> <mrow> <mi>O</mi> <mfenced> <msubsup> <mi>α</mi> <mi>s</mi> <mn>3</mn> </msubsup> </mfenced> </mrow> </math>   accuracy. We determine a set of  $$\hbox {aN}^3\hbox {LO}$$  <math> <mrow> <msup> <mtext>aN</mtext> <mn>3</mn> </msup> <mtext>LO</mtext> </mrow> </math>   PDFs by accounting both for the uncertainty on splitting functions due to the incomplete knowledge of  $$\hbox {N}^3\hbox {LO}$$  <math> <mrow> <msup> <mtext>N</mtext> <mn>3</mn> </msup> <mtext>LO</mtext> </mrow> </math>   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  $$\hbox {aN}^3\hbox {LO}$$  <math> <mrow> <msup> <mtext>aN</mtext> <mn>3</mn> </msup> <mtext>LO</mtext> </mrow> </math>   PDFs from the MSHT group. We examine the phenomenological impact of  $$\hbox {aN}^3\hbox {LO}$$  <math> <mrow> <msup> <mtext>aN</mtext> <mn>3</mn> </msup> <mtext>LO</mtext> </mrow> </math>   corrections on parton luminosities at the LHC, and give a first assessment of the impact of  $$\hbox {aN}^3\hbox {LO}$$  <math> <mrow> <msup> <mtext>aN</mtext> <mn>3</mn> </msup> <mtext>LO</mtext> </mrow> </math>   PDFs on the Higgs and Drell–Yan total production cross-sections. We find that the  $$\hbox {aN}^3\hbox {LO}$$  <math> <mrow> <msup> <mtext>aN</mtext> <mn>3</mn> </msup> <mtext>LO</mtext> </mrow> </math>   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.

Richard Ball

Andrea Barontini

Stefano Carrazza

Luigi Del Debbio

Tommaso Giani

Zahari Kassabov

Christopher Schwan

The path to  $$\hbox {N}^3\hbox {LO}$$  <math> <mrow> <msup> <mtext>N</mtext> <mn>3</mn> </msup> <mtext>LO</mtext> </mrow> </math>   parton distributions

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  $${\mathcal {O}}\left( \alpha \right) $$  <math> <mrow> <mi>O</mi> <mfenced> <mi>α</mi> </mfenced> </mrow> </math>  ,  $${\mathcal {O}}\left( \alpha \alpha _s\right) $$  <math> <mrow> <mi>O</mi> <mfenced> <mi>α</mi> <msub> <mi>α</mi> <mi>s</mi> </msub> </mfenced> </mrow> </math>  , and  $${\mathcal {O}}\left( \alpha ^2\right) $$  <math> <mrow> <mi>O</mi> <mfenced> <msup> <mi>α</mi> <mn>2</mn> </msup> </mfenced> </mrow> </math>   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.

Photons in the proton: implications for the LHC

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. PDF uncertainties on physical predictions in the data region are consequently either unchanged or moderately reduced by the inclusion of MHOUs.

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

Proton-proton collisions at the LHC generate a high-intensity collimated beam of neutrinos in the forward (beam) direction, characterised by energies of up to several TeV. The recent observation of LHC neutrinos by FASER $$\nu $$  <math> <mi>ν</mi> </math>   and SND@LHC signifies that this previously overlooked particle beam is now available for scientific investigation. Here we quantify the impact that neutrino deep-inelastic scattering (DIS) measurements at the LHC would have on the parton distributions (PDFs) of protons and heavy nuclei. We generate projections for DIS structure functions for FASER $$\nu $$  <math> <mi>ν</mi> </math>   and SND@LHC at Run III, as well as for the FASER $$\nu $$  <math> <mi>ν</mi> </math>  2, AdvSND, and FLArE experiments to be hosted at the proposed Forward Physics Facility (FPF) operating concurrently with the High-Luminosity LHC (HL-LHC). We determine that up to one million electron-neutrino and muon-neutrino DIS interactions within detector acceptance can be expected by the end of the HL-LHC, covering a kinematic region in x and  $$Q^2$$  <math> <msup> <mi>Q</mi> <mn>2</mn> </msup> </math>   overlapping with that of the Electron-Ion Collider. Including these DIS projections in global (n)PDF analyses, specifically PDF4LHC21, NNPDF4.0, and EPPS21, reveals a significant reduction in PDF uncertainties, in particular for strangeness and the up and down valence PDFs. We show that LHC neutrino data enable improved theoretical predictions for core processes at the HL-LHC, such as Higgs and weak gauge boson production. Our analysis demonstrates that exploiting the LHC neutrino beam effectively provides CERN with a “Neutrino-Ion Collider” without requiring modifications in its accelerator infrastructure.

Peter Krack

Toni Mäkelä

The LHC as a Neutrino-Ion Collider