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.

The dipole model provides a powerful framework for describing high-energy nuclear interactions, particularly in the regime of dense gluonic matter. However, accurately evolving the dipole–nucleus scattering amplitude remains a major computational challenge because it is governed by nonlinear QCD evolution equations. To address this, we investigate a machine learning (ML) model as an efficient surrogate for the conventional numerical evolution. These ML-based approximations dramatically reduce the computational cost of global analyses while maintaining the accuracy required to describe a broad range of experimental data. We systematically evaluate the ML results for accuracy, computational efficiency, and ability to capture essential features of dipole evolution in nuclear environments. These computational advancements will enable global analyses of diverse datasets within both the dipole and parton model frameworks, providing a more rigorous probe of nuclear structure in the dense regime. Comparing both descriptions within a common fitting framework can provide precise constraints on the gluon distributions and advance our understanding of the quark and gluon structure of nuclei, particularly in the small-x region.

We extend the QCD Parton Model analysis by employing a factorized nuclear structure model that explicitly accounts for both individual nucleons and correlated nucleon pairs. This novel framework establishes a paradigm that directly links the nuclear physics description of matter (in terms of protons and neutrons) to the particle physics schema (in terms of quarks and gluons). Our analysis of high-energy data from lepton Deep-Inelastic Scattering, Drell-Yan, and W/Z production simultaneously extracts the universal effective distribution of quarks and gluons inside correlated nucleon pairs, and their nucleus-specific fractions. The successful extraction of these universal distributions marks a significant advance in our understanding of nuclear structure, as it directly connects nucleon-level and parton-level quantities.

Deep Inelastic lepton-hadron Scattering (DIS) is a cornerstone of particle physics discovery and the precision measurement of the structure of matter. This document surveys the international DIS landscape, exploring current and future opportunities to continue this rich heritage, leading to new understandings and enabling discoveries. Of immediate relevance to the future of the field in Europe, the Large Hadron electron Collider (LHeC) offers an impactful bridge between the end of the HL-LHC and the beginning of the next CERN flagship project, both in terms of technology development and new scientific exploration from Higgs physics to the structure of the proton. More generally, the facilities described here cover energies from a few GeV to multiple TeV and address a wide range of topics, with unique sensitivity to Quantum Chromodynamics and hadron structure at their core. Additionally, they enhance the science programmes at hadron-hadron colliders. The fixed-target CEBAF programme at JLab probes nucleon and light ion structure at large x in novel ways, while high energy neutrino DIS is enabled at the FASER and SND@LHC experiments by the intense LHC beams. The Electron Ion Collider (EIC) is on course for deployment at Brookhaven in the early 2030s. Its science includes a 3-dimensional mapping of hadrons, leading to a thorough understanding of the mechanisms behind proton mass and spin. Adding the LHeC provides a Europe-based lepton-hadron frontier, including a complementary Higgs, top and electroweak programme to the HL-LHC, together with precise determinations of proton and nuclear structure in a kinematic range that improves HL-LHC sensitivities. In the longer term, plasma wakefield acceleration and the FCC offer possible major steps forward in centre-of-mass energy, extending into a low parton momentum-fraction domain where new strong interaction discoveries are guaranteed.

The approximate SACOT-chi scheme for heavy quark production in deep-inelastic scattering was initially formulated for the neutral current structure functions F2 and FL. We extend this approach to the charged current case (also including F3), and thereby complete the definitions for the most relevant inclusive structure functions. Furthermore, we implement these structure functions in the open-source code APFEL++ which provides fast numerical evaluations over a wide kinematic range; this addition to the APFEL++ code is publicly available, with details provided in the Appendix. This SACOT-chi implementation enables detailed numerical insights on the mass dependence of the structure functions and cross sections in the (x; Q2)-plane for both neutral and charged current processes. We consider kinematic regions relevant for the experimental measurements from fixed-target nu DIS experiments (NuTeV, CCFR, and Chorus) and HERA, and also projections for the upcoming EIC. In particular, the nu DIS experiments reveal a surprisingly strong dependence on the mass effects, offering valuable insights that may help resolve long-standing challenges in accurately describing these datasets.

This White Paper presents an overview of the current status and future perspective of QCD research, based on the community inputs and scientific conclusions from the 2022 Hot and Cold QCD Town Meeting. We present the progress made in the last decade toward a deep understanding of both the fundamental structure of the sub-atomic matter of nucleon and nucleus in cold QCD, and the hot QCD matter in heavy ion collisions. We identify key questions of QCD research and plausible paths to obtaining answers to those questions in the near future, hence defining priorities of our research over the coming decades.

Neutral current Drell-Yan (DY) lepton-pair production is considered in the framework of the Standard Model Effective Field Theory (SMEFT). Using the open-source fit platform xFitter, we investigate the impact of high-statistics measurements of the neutral current DY (NCDY) forward-backward asymmetry $A_{\rm{FB}}$ near the weak boson mass scale in the present and forthcoming stages of the Large Hadron Collider (LHC). Besides recovering earlier results on the $A_{\rm{FB}}$ sensitivity to parton distribution functions, we analyze the precision determination of $Z$-boson couplings to left-handed and right-handed $u$-quarks and $d$-quarks, and explore Beyond-Standard-Model contributions using the SMEFT framework. We comment on the role of the $A_{\rm{FB}}$ asymmetry for the electroweak SMEFT fit and precision $Z$-boson physics at the LHC and high-luminosity HL-LHC.

Motivated by the wide range of kinematics covered by current and planned deep-inelastic scattering (DIS) facilities, we revisit the formalism, practical implementation, and numerical impact of target mass corrections (TMCs) for DIS on unpolarized nuclear targets. An important aspect is that we only use nuclear and later partonic degrees of freedom, carefully avoiding a picture of the nucleus in terms of nucleons. After establishing that formulae used for individual nucleon targets (p,n), derived in the Operator Product Expansion (OPE) formalism, are indeed applicable to nuclear targets, we rewrite expressions for nuclear TMCs in terms of re-scaled (or averaged) kinematic variables. As a consequence, we find a representation for nuclear TMCs that is approximately independent of the nuclear target. We go on to construct a single-parameter fit for all nuclear targets that is in good numerical agreement with full computations of TMCs. We discuss in detail qualitative and quantitative differences between nuclear TMCs built in the OPE and the parton model formalisms, as well as give numerical predictions for current and future facilities.

We extend the QCD Parton Model analysis using a factorized nuclear structure model incorporating individual nucleons and pairs of correlated nucleons. Our analysis of high-energy data from lepton Deep-Inelastic Scattering, Drell-Yan and W/Z production simultaneously extracts the universal effective distribution of quarks and gluons inside correlated nucleon pairs, and their nucleus-specific fractions. Such successful extraction of these universal distributions marks a significant advance in our understanding of nuclear structure properties connecting nucleon- and parton-level quantities.

This document presents the initial scientific case for upgrading the Continuous Electron Beam Accelerator Facility (CEBAF) at Jefferson Lab (JLab) to 22 GeV. It is the result of a community effort, incorporating insights from a series of workshops conducted between March 2022 and April 2023. With a track record of over 25 years in delivering the world's most intense and precise multi-GeV electron beams, CEBAF's potential for a higher energy upgrade presents a unique opportunity for an innovative nuclear physics program, which seamlessly integrates a rich historical background with a promising future. The proposed physics program encompass a diverse range of investigations centered around the nonperturbative dynamics inherent in hadron structure and the exploration of strongly interacting systems. It builds upon the exceptional capabilities of CEBAF in high-luminosity operations, the availability of existing or planned Hall equipment, and recent advancements in accelerator technology. The proposed program cover various scientific topics, including Hadron Spectroscopy, Partonic Structure and Spin, Hadronization and Transverse Momentum, Spatial Structure, Mechanical Properties, Form Factors and Emergent Hadron Mass, Hadron-Quark Transition, and Nuclear Dynamics at Extreme Conditions, as well as QCD Confinement and Fundamental Symmetries. Each topic highlights the key measurements achievable at a 22 GeV CEBAF accelerator. Furthermore, this document outlines the significant physics outcomes and unique aspects of these programs that distinguish them from other existing or planned facilities. In summary, this document provides an exciting rationale for the energy upgrade of CEBAF to 22 GeV, outlining the transformative scientific potential that lies within reach, and the remarkable opportunities it offers for advancing our understanding of hadron physics and related fundamental phenomena.

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.

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 B\'ezier curves. This technique is implemented in a C++ module Fant\^omas 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.

We discuss the foundation for a new global nCTEQ nuclear PDF analysis, combining a number of our previous analyses into one consistent framework with updates to the underlying theoretical treatment as well as the addition of new available data. In particular, the new global release will be the first nCTEQ release containing neutrino DIS scattering data in a consistent manner together with JLab high-x DIS data and new LHC p-Pb data. These additions will improve the data-driven description of nuclear PDFs in new regions, especially the strange quark and the gluon PDF at low-x.

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.

Mass-dependent quark contributions are of great importance to DIS processes. The simplified-ACOT-scheme includes these effects over a wide range of momentum transfers up to next-to-leading order in QCD. In recent years an improvement in the case of neutral current DIS has been achieved by using zero-mass contributions up to next-to-next-to-leading order (NNLO) with massive phase-space constraints. In this work, we extend this approach to the case of charged current DIS and provide an implementation in the open-source code APFEL++. The increased precision will be valuable for ongoing and future neutrino programs, the Electron-Ion-Collider and the studies of partonic substructure of hadrons and nuclei. A highly efficient implementation using gridding techniques extends the applicability of the code to the determination of parton distribution functions (PDFs).

method. We then apply the method to determine the 87Y(n, γ ) cross section, which has not been measured directly. The work was carried out in the context of an LLNL L2 Milestone. This report addresses the theory aspects of the milestone. A complementary document summarizes the experimental efforts [1].

and GRETINA a 1{pi} detector is under construction. However, the momentum in developing this technology to its full potential must continue towards GRETA, a full 4{pi} calorimeter. GRETA will carry {gamma}-ray spectroscopy into the next generation where it will be needed to fully exploit the science opportunities at radioactive beam facilities and increase the reach of stable beam facilities. In addition, {gamma}-ray tracking technology will have important applications for science, medicine, and homeland security.

We report on a new framework to parametrize parton distribution functions (PDFs) and other hadronic nonperturbative functions using polynomial functions realized by B\'ezier curves. B\'ezier 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.

Nuclear parton distribution functions (nPDFs) are crucial in studying nuclear structure and high-energy nuclear collisions. nPDFs have been determined via 'global QCD analyses', in which the nPDF-dependent predictions for a given process are compared with their actual measurements. One of the challenging parts of nPDF extractions is the estimation of uncertainties. The most common approach for this purpose is the Hessian method, which, however, has certain shortcomings, especially in the case of weaker data constraints. Here, we will show a case study for an alternative approach where nPDF uncertainties are estimated using Markov Chain Monte Carlo (MCMC) methods.

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.