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The proton, one of the components of atomic nuclei, is composed of fundamental particles called quarks and gluons. Gluons are the carriers of the force that binds quarks together, and free quarks are never found in isolation—that is, they are confined within the composite particles in which they reside. The origin of quark confinement is one of the most important questions in modern particle and nuclear physics because confinement is at the core of what makes the proton a stable particle and thus provides stability to the Universe. The internal quark structure of the proton is revealed by deeply virtual Compton scattering 1 , 2 , a process in which electrons are scattered off quarks inside the protons, which  subsequently emit high-energy photons, which are detected in coincidence with the scattered electrons and recoil protons. Here we report a measurement of the pressure distribution experienced by the quarks in the proton. We find a strong repulsive pressure near the centre of the proton (up to 0.6 femtometres) and a binding pressure at greater distances. The average peak pressure near the centre is about 10 35 pascals, which exceeds the pressure estimated for the most densely packed known objects in the Universe, neutron stars 3 . This work opens up a new area of research on the fundamental gravitational properties of protons, neutrons and nuclei, which can provide access to their physical radii, the internal shear forces acting on the quarks and their pressure distributions. Measurements of the quark pressure distribution in the proton reveal a strong repulsive pressure near the proton’s centre (stronger than the pressure in neutron stars) and a binding pressure at greater distances.

The proton, one of the components of atomic nuclei, is composed of fundamental particles called quarks and gluons. Gluons are the carriers of the force that binds quarks together, and free quarks are never found in isolation--that is, they are confined within the composite particles in which they reside. The origin of quark confinement is one of the most important questions in modern particle and nuclear physics because confinement is at the core of what makes the proton a stable particle and thus provides stability to the Universe. The internal quark structure of the proton is revealed by deeply virtual Compton scattering.sup.1,2, a process in which electrons are scattered off quarks inside the protons, which subsequently emit high-energy photons, which are detected in coincidence with the scattered electrons and recoil protons. Here we report a measurement of the pressure distribution experienced by the quarks in the proton. We find a strong repulsive pressure near the centre of the proton (up to 0.6 femtometres) and a binding pressure at greater distances. The average peak pressure near the centre is about 10.sup.35 pascals, which exceeds the pressure estimated for the most densely packed known objects in the Universe, neutron stars.sup.3. This work opens up a new area of research on the fundamental gravitational properties of protons, neutrons and nuclei, which can provide access to their physical radii, the internal shear forces acting on the quarks and their pressure distributions.

The proton, one of the components of atomic nuclei, is composed of fundamental particles called quarks and gluons. Gluons are the carriers of the force that binds quarks together, and free quarks are never found in isolation--that is, they are confined within the composite particles in which they reside. The origin of quark confinement is one of the most important questions in modern particle and nuclear physics because confinement is at the core of what makes the proton a stable particle and thus provides stability to the Universe. The internal quark structure of the proton is revealed by deeply virtual Compton scattering.sup.1,2, a process in which electrons are scattered off quarks inside the protons, which subsequently emit high-energy photons, which are detected in coincidence with the scattered electrons and recoil protons. Here we report a measurement of the pressure distribution experienced by the quarks in the proton. We find a strong repulsive pressure near the centre of the proton (up to 0.6 femtometres) and a binding pressure at greater distances. The average peak pressure near the centre is about 10.sup.35 pascals, which exceeds the pressure estimated for the most densely packed known objects in the Universe, neutron stars.sup.3. This work opens up a new area of research on the fundamental gravitational properties of protons, neutrons and nuclei, which can provide access to their physical radii, the internal shear forces acting on the quarks and their pressure distributions.

The proton, one of the components of atomic nuclei, is composed of fundamental particles called quarks and gluons. Gluons are the carriers of the force that binds quarks together, and free quarks are never found in isolation--that is, they are confined within the composite particles in which they reside. The origin of quark confinement is one of the most important questions in modern particle and nuclear physics because confinement is at the core of what makes the proton a stable particle and thus provides stability to the Universe. The internal quark structure of the proton is revealed by deeply virtual Compton scattering.sup.1,2, a process in which electrons are scattered off quarks inside the protons, which subsequently emit high-energy photons, which are detected in coincidence with the scattered electrons and recoil protons. Here we report a measurement of the pressure distribution experienced by the quarks in the proton. We find a strong repulsive pressure near the centre of the proton (up to 0.6 femtometres) and a binding pressure at greater distances. The average peak pressure near the centre is about 10.sup.35 pascals, which exceeds the pressure estimated for the most densely packed known objects in the Universe, neutron stars.sup.3. This work opens up a new area of research on the fundamental gravitational properties of protons, neutrons and nuclei, which can provide access to their physical radii, the internal shear forces acting on the quarks and their pressure distributions.

The double-spin-polarization observable$${\\mathbb {E}}$$E for$$\\vec {\\gamma }\\vec {p}\\rightarrow p\\pi ^0$$γ → p → → p π 0 has been measured with the CEBAF Large Acceptance Spectrometer (CLAS) at photon beam energies$$E_\\gamma $$E γ from 0.367 to$$2.173~\\textrm{GeV}$$2.173 GeV (corresponding to center-of-mass energies from 1.240 to$$2.200~\\textrm{GeV}$$2.200 GeV ) for pion center-of-mass angles,$$\\cos \\theta _{\\pi ^0}^{c.m.}$$cos θ π 0 c . m . , between$$-$$- 0.86 and 0.82. These new CLAS measurements cover a broader energy range and have smaller uncertainties compared to previous CBELSA data and provide an important independent check on systematics. These measurements are compared to predictions as well as new global fits from The George Washington University, Mainz, and Bonn-Gatchina groups. Their inclusion in multipole analyses will allow us to refine our understanding of the single-pion production contribution to the Gerasimov-Drell-Hearn sum rule and improve the determination of resonance properties, which will be presented in a future publication.

The double-spin-polarization observable $\\mathbb{E}$ for $\\vec{\\gamma}\\vec{p}\\to p\\pi^0$ has been measured with the CEBAF Large Acceptance Spectrometer (CLAS) at photon beam energies $E_\\gamma$ from 0.367 to $2.173~\\mathrm{GeV}$ (corresponding to center-of-mass energies from 1.240 to $2.200~\\mathrm{GeV}$) for pion center-of-mass angles, $\\cos\\theta_{\\pi^0}^{c.m.}$, between -0.86 and 0.82. These new CLAS measurements cover a broader energy range and have smaller uncertainties compared to previous CBELSA data and provide an important independent check on systematics. These measurements are compared to predictions as well as new global fits from The George Washington University, Mainz, and Bonn-Gatchina groups. Their inclusion in multipole analyses will refine our understanding of the single-pion production contribution to the Gerasimov-Drell-Hearn sum rule and improve the determination of resonance properties.

We present the first determination of the proton mechanical radius. The result was obtained by employing a novel theoretical approach that connects experimental data of deeply virtual Compton scattering with the spin = 2 interaction that is characteristic of gravity coupling with matter. We find that the proton mechanical radius is significantly smaller than its charge radius, consistent with the latest Lattice QCD computation.

The manuscript focuses on the high impact science of the EIC with objective to identify a portion of the science program for QCD precision studies that requires or greatly benefits from high luminosity and low center-of-mass energies. The science topics include (1) Generalized Parton Distributions, 3D imagining and mechanical properties of the nucleon (2) mass and spin of the nucleon (3) Momentum dependence of the nucleon in semi-inclusive deep inelastic scattering (4) Exotic meson spectroscopy (5) Science highlights of nuclei (6) Precision studies of Lattice QCD in the EIC era (7) Science of far-forward particle detection (8) Radiative effects and corrections (9) Artificial Intelligence (10) EIC interaction regions for high impact science program with discovery potential. This paper documents the scientific basis for supporting such a program and helps to define the path toward the realization of the second EIC interaction region.

The physics of the gravitational form factors of the proton, and their understanding within quantum chromodynamics, has advanced significantly in the past two decades through both theory and experiment. This Colloquium provides an overview of this progress, highlights the physical insights unveiled by studies of gravitational form factors, and reviews their interpretation in terms of the mechanical properties of the proton.

We report on the first determination of the shear forces quarks inside the proton from experimental data on deeply virtual Compton scattering. The maximum shear force of approximately 40 MeV/fm occurs near 0.6 fm from the proton center, indicating where confinement forces may be strongest. On the macroscopic scale of the earth surface, this force corresponds to the weight of a mass of about 650 kg. The shear forces in the proton reverse direction at r = 0.45 fm from the center.