We present a quantitative assessment of the anticipated impact of future Electron-Ion Collider (EIC) measurements on the extraction of parton-to-pion fragmentation functions (FFs). Our analysis combines simulated semi-inclusive deep-inelastic scattering (SIDIS) pseudo-data at EIC energies of 45 GeV and 140 GeV with existing single-inclusive electron-positron annihilation (SIA) and SIDIS experimental data. The pion fragmentation functions are determined at next-to-leading-order (NLO) accuracy using a perturbative quantum chromodynamics framework and a neural network parametrization. Uncertainties are rigorously estimated through Monte Carlo sampling, accounting for both experimental errors and variations in input parton distribution functions. Our results demonstrate that incorporating EIC pseudo-data reduces their uncertainties, especially at medium- to-large momentum fractions (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>z</mi></math>). This improvement is particularly pronounced for the gluon and selected quark FFs, highlighting the substantial role that EIC measurements will play in achieving high-precision extractions of FFs and informing future experimental and theoretical developments in collider physics.

Iran

United Arab Emirates

Maryam Soleymaninia

Poland

Hamzeh Khanpour

Majid Azizi

Italy

Hadi Hashamipour

Improved constraints on pion fragmentation functions from simulated electron-ion collider data

The proton’s internal structure is characterized not only by its charge and magnetic distribution, but also by its mechanical and mass properties, which are encoded in the energy-momentum tensor (EMT) of quantum chromodynamics (QCD). These properties provide insights into the spatial distributions of energy, pressure, and shear forces within the proton. Understanding the proton’s internal structure, including properties such as its mechanical and mass radii, is essential for unraveling the complex interplay between quarks and gluons that govern its stability and dynamics. In this study, we investigate the gravitational form factors (GFFs) of the proton, particularly the D term, which encodes key information about the internal stress distribution, pressure, and shear forces within the nucleon. Using a model for skewness-dependent generalized parton distributions constructed from the double-distribution representation, we extract the quark contribution to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></math> GFF of the EMT by analyzing available data on Compton form factors. We then employ this extracted GFF to explore the mechanical properties of the proton, including its mechanical and mass radii, as well as the internal pressure and shear force distributions. Our results provide new insights into the proton’s internal structure and contribute to the broader understanding of nucleon properties.

Muhammad Goharipour

H. Fatehi

Fatemeh Irani

Türkiye

K. Azizi

JINR

S.V. Goloskokov

Mechanical properties of the nucleon from the generalized parton distributions

The proton-radius puzzle refers to the discrepancy observed in measurements of the proton's charge radius when using different methods. This inconsistency has prompted extensive research and debate within the physics community, as it challenges the understanding of quantum electrodynamics and the fundamental properties of protons. In the present study, we determine the charge and magnetic radii of the proton and neutron through a global analysis of the generalized parton distributions (GPDs) at zero skewness. We emphasize the importance of a simultaneous analysis of all available experimental data related to nucleon radii, rather than relying on individual experiments, specific observables, or limited kinematic regions. This comprehensive approach ensures robust and consistent results, avoiding values that are either too small or too large. Our analysis yields the following results: <math altimg='si1.svg'><msub><mrow><mi>r</mi></mrow><mrow><mi>p</mi><mi>E</mi></mrow></msub><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mn>0.8558</mn><mo>&#177;</mo><mn>0.0135</mn><mspace width='0.25em' /><mtext mathvariant='normal'>fm</mtext></math>, <math altimg='si2.svg'><msub><mrow><mi>r</mi></mrow><mrow><mi>p</mi><mi>M</mi></mrow></msub><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mn>0.8268</mn><mo>&#177;</mo><mn>0.0533</mn><mspace width='0.25em' /><mtext mathvariant='normal'>fm</mtext></math>, <math altimg='si3.svg'><mrow><mo stretchy='true'>&#9001;</mo><msubsup><mrow><mi>r</mi></mrow><mrow><mi>n</mi><mi>E</mi></mrow><mrow><mn>2</mn></mrow></msubsup><mo stretchy='true'>&#9002;</mo></mrow><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo><mn>0.1181</mn><mo>&#177;</mo><mn>0.0270</mn><mspace width='0.25em' /><msup><mrow><mtext mathvariant='normal'>fm</mtext></mrow><mrow><mn>2</mn></mrow></msup></math>, and <math altimg='si4.svg'><msub><mrow><mi>r</mi></mrow><mrow><mi>n</mi><mi>M</mi></mrow></msub><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mn>0.8367</mn><mo>&#177;</mo><mn>0.0845</mn><mspace width='0.25em' /><mtext mathvariant='normal'>fm</mtext></math>.

The charge and magnetic radii of the nucleons from the generalized parton distributions

We present new parton distribution functions (PDFs) at next-to-leading order and next-to-next-to-leading order in perturbative QCD, derived from a comprehensive QCD analysis of high-precision datasets from combined HERA deep-inelastic scattering, the Tevatron, and the LHC. To improve constraints on quark flavor separation, we incorporate Drell-Yan pair production data, which provides critical sensitivity to the quark distributions. In addition, we include the latest <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>W</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi></math> boson production data from the CDF, D0, ATLAS, and CMS collaborations, further refining both quark and gluon distributions. Our nominal QCD fit integrates these datasets and examines the resulting impact on the PDFs and their associated uncertainties. Uncertainties in the PDFs are quantified using the Hessian method, ensuring robust error estimates. Furthermore, we explore the sensitivity of the strong coupling constant, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>α</mi><mi>s</mi></msub><mo stretchy="false">(</mo><msubsup><mi>M</mi><mi>Z</mi><mn>2</mn></msubsup><mo stretchy="false">)</mo></math>, and proton PDFs in light of the projected measurements from the Electron-Ion Collider, where improvements in precision are expected. The analysis also investigates the effects of inclusive jet and dijet production data, which provide enhanced constraints on the gluon PDF and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>α</mi><mi>s</mi></msub><mo stretchy="false">(</mo><msubsup><mi>M</mi><mi>Z</mi><mn>2</mn></msubsup><mo stretchy="false">)</mo></math>.

Germany

Maral Salajegheh

China

Ulf-G. Meißner

Revisiting constraints on proton PDFs from HERA DIS, Drell-Yan, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>W</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi></math> boson production, and projected EIC measurements

In this study, we revisit the extraction of parton-to-<math><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup></math> hadron fragmentation functions, named FF24-<math><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup></math>, focusing on both next-to-leading-order and next-to-next-to-leading-order accuracy in perturbative QCD. Our approach involves the analysis of single inclusive electron-positron annihilation (SIA) data. The two key improvements are, on the one hand, the incorporation of the latest experimental data from the BESIII experiment and, on the other hand, the adoption of neural networks in the fitting procedure. To address experimental uncertainties, the Monte Carlo method is employed. Our investigation also explores the impact of hadron mass corrections on the description of SIA data, spanning a broad kinematic regime with a particular emphasis on the range of small <math><mi>z</mi></math> values. The theory prediction for <math><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup></math> production at both NLO and NNLO accuracy exhibits good agreement with experimental data within their respective uncertainties.

Hubert Spiesberger

Georgia

Determination of <math><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup></math> fragmentation functions including BESIII measurements and using neural networks

It is well-established now that the generalized parton distributions (GPDs) at zero skewness are playing important roles in some physical process such as elastic electron-nucleon scattering, elastic (anti)neutrino-nucleon scattering, and wide-angle Compton scattering (WACS) via various types of form factors (FFs). In this study, we are going to utilize the recent JLab measurements of the elastic electron-nucleon scattering reduced cross section, namely GMp12, as a touchstone to unravel the tension observed between the measurements of the WACS cross section and the data of the proton magnetic FF <math><msubsup><mi>G</mi><mi>M</mi><mi>p</mi></msubsup></math>. We also investigate the impact of GMp12 data on valence unpolarized GPDs <math><msubsup><mi>H</mi><mi>v</mi><mi>q</mi></msubsup></math> and <math><msubsup><mi>E</mi><mi>v</mi><mi>q</mi></msubsup></math> at zero skewness by performing some <math><msup><mi>χ</mi><mn>2</mn></msup></math> analyses of the related experimental data. By calculating the electric and scalar quadrupole ratios, <math><msub><mi>R</mi><mrow><mi>EM</mi></mrow></msub></math> and <math><msub><mi>R</mi><mi>SM</mi></msub></math>, and magnetic transition FF <math><msubsup><mi>G</mi><mi>M</mi><mo>*</mo></msubsup><mo>/</mo><mn>3</mn><msub><mi>G</mi><mi>D</mi></msub></math> related to the nucleon-to-delta (<math><mi>N</mi><mo>→</mo><mi>Δ</mi></math>) transition using the extracted GPDs and comparing the results with corresponding experimental measurements, we show that our results are in an excellent consistency with experiments, indicating the universality property of GPDs. We emphasize that the inclusion of these data in the future analysis of GPDs can significantly affect the extracted GPDs especially their uncertainties at smaller values of <math><msup><mi>Q</mi><mn>2</mn></msup></math>.

Impact of JLab data on the determination of GPDs at zero skewness and new insights from transition form factors <math><mi>N</mi><mo>→</mo><mi>Δ</mi></math>

We investigate the impact of the new measurement of the antineutrino-proton scattering cross section from the MINERvA Collaboration on generalized parton distributions (GPDs), particularly the polarized GPDs denoted as <math><mrow><msup><mrow><mover><mrow><mi>H</mi></mrow><mrow><mo>˜</mo></mrow></mover></mrow><mrow><mi>q</mi></mrow></msup></mrow></math>. To achieve this, we perform some QCD analyses of the MINERvA data, in addition to all available data of the proton’s axial form factors. We demonstrate that MINERvA data lead to consistent results with other related experimental data, confirming the universality of GPDs. Our results indicate that MINERvA data can impose new constraints on GPDs, particularly on <math><mrow><msup><mrow><mover><mrow><mi>H</mi></mrow><mrow><mo>˜</mo></mrow></mover></mrow><mrow><mi>q</mi></mrow></msup></mrow></math>. Our predictions for the proton’s axial charge radius, WACS cross section, and axial form factor show good consistency with those of other studies and measurements. This leads us to conclude that the result of a more comprehensive analysis, considering all related experimental data, is not only reasonable but also more reliable, even in light of existing tensions among the data. The present study can be considered as a guideline for performing a new and comprehensive QCD global analysis of GPDs including the MINERvA measurements like that presented in Hashamipour et al. [Generalized parton distributions at zero skewness, Phys. Rev. D 107, 096005 (2023).].

Impact of recent MINERvA measurement of the antineutrino-proton scattering cross section on the generalized parton distributions

We present an updated set of SKMHS diffractive parton distribution functions (PDFs). In addition to the diffractive deep-inelastic scattering (diffractive DIS) datasets, the recent diffractive dijet cross-section measurement by the H1 experiment from the HERA collider are added to the data sample. The new set of diffractive PDFs, entitled SKMHS23 and SKMHS23-dijet, are presented at next-to-leading order (NLO) and next-to-next-to-leading order (NNLO) accuracy in perturbative QCD. Since the gluons directly contribute to jet production through the boson-gluon fusion process, the data on diffractive dijet production in inclusive DIS help constrain the gluon density, allowing for the determination of both the quark and gluon densities with better accuracy. The NLO and NNLO theory predictions calculated using both SKMHS23 and SKMHS23-dijet are compared to the analyzed data showing excellent agreement. The effect arising from the inclusion of diffractive dijet data and higher-order QCD corrections on the extracted diffractive PDFs and data/theory agreements are clearly examined and discussed.

Determination of diffractive PDFs from a global QCD analysis of inclusive diffractive DIS and dijet cross-section measurements at HERA

We present a new determination of the generalized parton distributions (GPDs) with their uncertainties at zero skewness, <math><mrow><mi>ξ</mi><mo>=</mo><mn>0</mn></mrow></math>, through a simultaneous analysis of all available experimental data of the nucleon electromagnetic form factors (FFs), nucleon charge and magnetic radii, proton axial FFs (AFFs), and wide-angle Compton scattering (WACS) cross sections for the first time, and we investigate whether there is any tension between these data. This can be considered the most comprehensive analysis of GPDs at <math><mi>ξ</mi><mo>=</mo><mn>0</mn></math> performed so far. We show that such an analysis provides the simultaneous determination of three kinds of GPDs: namely <math><msup><mi>H</mi><mi>q</mi></msup></math>, <math><msup><mover><mi>H</mi><mo>˜</mo></mover><mi>q</mi></msup></math>, and <math><msup><mi>E</mi><mi>q</mi></msup></math>, considering also the sea-quark contributions. As a result, we find that the inclusion of the WACS and AFF data at larger values of the momentum transfer squared <math><msup><mi>Q</mi><mn>2</mn></msup><mo>=</mo><mo>−</mo><mi>t</mi></math> can put new constraints on GPDs and change them drastically in some cases. We show that there is a considerable tension between the WACS and the proton magnetic form factor (<math><msubsup><mi>G</mi><mi>M</mi><mi>p</mi></msubsup></math>) data, especially at larger values of <math><mo>−</mo><mi>t</mi></math>. However, we indicate that the results for the gravitational FF <math><msub><mi>M</mi><mn>2</mn></msub></math> and the proton total angular momentum <math><msup><mi>J</mi><mi>p</mi></msup></math> calculated using the extracted GPDs are in relatively good agreement with the light-cone QCD sum rules (LCSRs) and lattice QCD predictions when the sea-quark contributions are considered and both WACS and <math><msubsup><mi>G</mi><mi>M</mi><mi>p</mi></msubsup></math> data are included in the analyses simultaneously.

S. V. Goloskokov

Generalized parton distributions at zero skewness

We present SKMHS22, a new set of diffractive parton distribution functions (PDFs) and their uncertainties at next-to-leading-order and next-to-next-to-leading-order accuracy in perturbative QCD within the xFitter framework. We describe all available diffractive DIS datasets from HERA and the most recent high-precision H1/ZEUS combined measurements considering three different scenarios. First, we extract the diffractive PDFs considering the standard twist-2 contribution. Then, we include the twist-4 correction from the longitudinal virtual photons. Finally, the contribution of subleading Reggeon exchange to the structure-function <math><msubsup><mi>F</mi><mn>2</mn><mi>D</mi></msubsup></math> is also examined. For the contribution of heavy flavors, we utilize the Thorne-Roberts general mass variable number scheme. We show that for those corrections, in particular, the twist-4 contribution allows us to include the high-<math><mi>β</mi></math> region and leads to a better description of the diffractive DIS datasets. We find that the inclusion of the subleading Reggeon exchange significantly improves the description of the diffractive DIS cross-section measurements. We then investigate the stability of the SKMHS22 QCD fit upon the inclusion of higher-order QCD corrections and show that it slightly improves the description of the data. The resulting sets are in good agreement with all diffractive DIS data analyzed, which cover a wider kinematical range than in previous fits. The SKMHS22 diffractive PDFs sets presented in this work are available via the LHAPDF interface. We also make suggestions for future research in this area.