Welcome

• Kazuhiro Watanabe (Seikei University)

3D tomography of hadrons with hadron and lepton beams

• Shunzo Kumano (Japan Women's University / KEK)

Form factors defined by matrix elements of quark and gluon energy-momentum tensors are called gravitational form factors. They used to be considered as purely academic quantities without any experimental measurement because the gravitational interactions are extremely small in comparison with strong, electromagnetic, and weak interactions. However, due to recent developments of the hadron-tomography field, it became possible to determine these form factors from spacelike generalized parton distributions (GPDs) and their s-t crossed ones, generalized distribution amplitudes (GDAs). The GDAs could be called timelike GPDs. The spacelike and timelike GPDs are investigated in charged-lepton-scattering processes and electron-positron collisions, typically, by deeply virtual Compton scattering and two-photon processes, respectively [1]. In addition, hadron-accelerator [2] and neutrino [3] facility measurements will become possible in the near future. In this talk, I explain these GPD projects. *S. Kumano was partially supported by Japan Society for the Promotion of Science (JSPS) Grants-in-Aid for Scientific Research (KAKENHI) Grant Number 19K03830.

Deep-inelastic scattering and Drell-Yan process for the 3D structure of the nucleon

• Toshi-Aki Shibata (Nihon University)

An overview of the study of the 3D structure of the nucleon is described. Both the longitudinal and transverse structures of the nucleon have been investigated with various experimental methods. The longitudinal structure or helicity distribution was studied first as the cross section of polarized deep-inelastic scattering was formulated with quark-parton model. The result reported by EMC in the papers in 1988 and 1989 showed that the contribution of spin of quarks and anti-quarks to the proton spin is only (12 +- 9 +- 14)%. The result was confirmed by the experiments in 1990's and later. Spin is one of the quantum numbers of the nucleon. The concept of 'valence quark' was questioned because the valence quarks were supposed to determine all the quantum numbers of the nucleon. Sea quarks are quarks and anti-quarks generated by the gluon dissociation inside the nucleon. Those sea quarks could also contribute to the nucleon spin. Gluon spin contribution was studied by proton-proton collisions and deep-inelastic scattering. The transverse-momentum-dependent parton distributions (TMDs) and the orbital angular momenta of partons are another subjects under study. The single-spin asymmetry in meson productions was observed with increasing center-of-mass energy up to RHIC. Sivers- and Collins-asymmetries were separately identified by sin( phi - phi_S ) and sin( phi + phi_S ) modulations of the azimuthal distributions by HERMES in 2005. The coincidence measurement of the scattered lepton and produced hadrons turned out to be the effective method. Exclusive photon and meson productions were measured for generalized parton distributions. The deep-inelastic scattering is sensitive to the sum of parton distributions of quarks and anti-quarks while the Drell-Yan process is sensitive to the products of the two. The properties of anti-quarks can be studied with a combination of these two complementary approaches. The evolution and perspective of the study with these experimental methods are discussed.

Study of 3D nucleon structure at the J-PARC π20 beamline

• Tomida Natsuki (Kyoto University)

One of the keys to understand 3D nucleon structure is precise measurements of Generalized Parton Distribution Functions (GPDs). Measurements in different reactions help to verify universality of GPDs and derive GPDs in wide kinematic region. Hadron induced exclusive reactions are complementary to lepton induced reactions such as deeply virtual Compton scattering (DVCS) and deeply virtual meson production (DVMP). In the J-PARC hadron experimental hall, measurements of GPDs using hadron beam are planned. At the high momentum beam line, 30 GeV/c primary proton beam from the J-PARC Main Ring is derived. In addition, positive and negative π/K/p secondary beam up to 20 GeV/c will be delivered by installing a new production target. The secondary beam line is called π20 beam line. At the π20 beam line, measurements of the exclusive Drell-Yan reaction (π-p→γ*n→μ+μ-n) and 2→3 reactions (such as pp→pπ+n) are planned to access GPDs. The medium beam momentum of the π20 beam line is suited for the measurements of those reactions since cross sections of these reactions decrease with beam momentum. A new high-resolution, high-rate capable spectrometer is under construction. The new spectrometer enables the first measurements of above exclusive reactions thanks to a good momentum resolution under high rate. We will report details and prospects of these experiments.

Single diffractive hard exclusive processes for the study of generalized parton distributions

• Zhite Yu (Jefferson Lab)

Generalized parton distributions (GPDs) are important non-perturbative functions that provide tomographic images of the partonic structures of hadrons. We introduce a type of exclusive processes for a better study of GPDs, which we refer to as single diffractive hard exclusive processes (SDHEPs), and give a general proof for their factorization into GPDs. We demonstrate that the SDHEP is not only sufficiently generic to cover all known processes but also well motivated for searching for new processes for extracting GPDs. Importantly, we also examine the sensitivity of the SDHEP to the parton momentum fraction x dependence of GPDs, and demonstrate quantitatively with two processes that can be readily measured at J-PARC/AMBER and JLab, respectively. *This work is supported in part by the US Department of Energy (DOE) Contract No. DE-AC05- 06OR23177, under which Jefferson Science Associates, LLC operates Jefferson Lab. The work of Z.Y. at MSU is partially supported by the U.S. National Science Foun- dation under Grant No. PHY-2013791, and the fund from the Wu-Ki Tung endowed chair in particle physics.

SoLID Double Deeply Virtual Scattering in Hall A Jefferson Laboratory

• Alexandre Camsonne (Jefferson Lab)

The SoLID spectrometer being developped in Hall A at Jefferson Laboratory is a solenoidal spectrometer designed to be able to run at high luminosity up to 10^38 cm-2.s-1. Such luminosity allows to measure low cross section processes such as Double Deeply Virtual Compton Scattering experiment, which would allow to map Generalized Parton Distribution at different skewness compared to existing data from Deeply Virtual Compton Scattering. I will present the proposal for a DDVCS experiment in parallel of the J/Psi SoLID experiment and possible future dedicated experiments at 11 and 22 GeV.

DVCS and HEMP at COMPASS experiment for GPD studies

• Takahiro Iwata

COMPASS is a fixed target experiment with a high energy muon beam from the SPS at CERN. One of the important aims of the experiment is to study the 3D structure of the nucleon from the point of view of Generalized Parton Distributions(GPD). In the experiment, Deeply Virtual Compaton Scattering(DVCS) and Hard Exclusive Meson Production(HEMP) processes have been studied intensively. Following the COMPASS setup , the experimental results obtained so far on the DVCS and the HEMP will be presented. The results include the cross section of the DVCS and the exclusive neutral pion production and the transverse target spin asymmetries and spin density matrix elements for the exclusive production of rho and omega mesons. Based on the results on the t-slope of the DVCS, we discuss about the transverse extenstion of partons in nucleon. The results for the HEMP, constraints for the GPD models are given.

Recent progress on nucleon form factors in lattice QCD at the physical point

• Shoichi Sasaki (Tohoku University)

We present results for the isovector axial charge and root-mean-square (RMS) radii of the nucleon obtained from 2+1 flavor lattice QCD at the physical point with a large spatial extent of about 10 fm. Our calculations are performed with the PACS10 gauge configurations generated by the PACS Collaboration with the six stout-smeared O(a) improved Wilson-clover quark action and Iwasaki gauge action at beta=1.82 and 2.00 corresponding to lattice spacings of 0.085 fm and 0.063 fm respectively. We first evaluate the axial charge, which is one of the most important pieces of information on the nucleon structure. Moreover, we also calculate the nucleon elastic form factors and determine three kinds of isovector RMS radii such as electric, magnetic and axial ones at the two lattice spacings. We finally discuss the discretization uncertainties on the axial charge and isovector RMS radii towards the continuum limit.

Accessing x-dependent GPDs from lattice QCD

• Martha Constantinou (Temple University)

Generalized parton distributions (GPDs) are important quantities that characterize the 3-D structure of hadrons, and complement the information extracted from TMDs. They provide information about the partons' momentum distribution and also on their distribution in position space. Most of the information from lattice QCD is on the Mellin moments of GPDs, namely form factors and their generalizations. Recent developments in calculations of matrix elements of boosted hadrons coupled with non-local operators opened a new direction for extracting the x dependence of GPDs. *U.S. Department of Energy, Office of Nuclear Physics, Early Career Award under Grant No. DE-SC0020405U.S. Department of Energy, Office of Nuclear Physics, Quark-Gluon Tomography topical collaboration under Grant No. DE-SC0023646