Determining the gluonic gravitational form factors of the proton.

The proton is one of the main building blocks of all visible matter in the Universe1. Among its intrinsic properties are its electric charge, mass and spin2. These properties emerge from the complex dynamics of its fundamental constituents-quarks and gluons-described by the theory of quantum chromodynamics3-5. The electric charge and spin of protons, which are shared among the quarks, have been investigated previously using electron scattering2. An example is the highly precise measurement of the electric charge radius of the proton6. By contrast, little is known about the inner mass density of the proton, which is dominated by the energy carried by gluons. Gluons are hard to access using electron scattering because they do not carry an electromagnetic charge. Here we investigated the gravitational density of gluons using a small colour dipole, through the threshold photoproduction of the J/ψ particle. We determined the gluonic gravitational form factors of the proton7,8 from our measurement. We used a variety of models9-11 and determined, in all cases, a mass radius that is notably smaller than the electric charge radius. In some, but not all cases, depending on the model, the determined radius agrees well with first-principle predictions from lattice quantum chromodynamics12. This work paves the way for a deeper understanding of the salient role of gluons in providing gravitational mass to visible matter.

A small proton charge radius from an electron-proton scattering experiment.

Elastic electron-proton scattering (e-p) and the spectroscopy of hydrogen atoms are the two methods traditionally used to determine the proton charge radius, rp. In 2010, a new method using muonic hydrogen atoms1 found a substantial discrepancy compared with previous results2, which became known as the 'proton radius puzzle'. Despite experimental and theoretical efforts, the puzzle remains unresolved. In fact, there is a discrepancy between the two most recent spectroscopic measurements conducted on ordinary hydrogen3,4. Here we report on the proton charge radius experiment at Jefferson Laboratory (PRad), a high-precision e-p experiment that was established after the discrepancy was identified. We used a magnetic-spectrometer-free method along with a windowless hydrogen gas target, which overcame several limitations of previous e-p experiments and enabled measurements at very small forward-scattering angles. Our result, rp = 0.831 ± 0.007stat ± 0.012syst femtometres, is smaller than the most recent high-precision e-p measurement5 and 2.7 standard deviations smaller than the average of all e-p experimental results6. The smaller rp we have now measured supports the value found by two previous muonic hydrogen experiments1,7. In addition, our finding agrees with the revised value (announced in 2019) for the Rydberg constant8-one of the most accurately evaluated fundamental constants in physics.

Determination of the

We report the first measurement of the parity-violating elastic electron scattering asymmetry on ^{27}Al. The ^{27}Al elastic asymmetry is A_{PV}=2.16±0.11(stat)±0.16(syst) ppm, and was measured at ⟨Q^{2}⟩=0.02357±0.00010 GeV^{2}, ⟨θ_{lab}⟩=7.61°±0.02°, and ⟨E_{lab}⟩=1.157 GeV with the Q_{weak} apparatus at Jefferson Lab. Predictions using a simple Born approximation as well as more sophisticated distorted-wave calculations are in good agreement with this result. From this asymmetry the ^{27}Al neutron radius R_{n}=2.89±0.12 fm was determined using a many-models correlation technique. The corresponding neutron skin thickness R_{n}-R_{p}=-0.04±0.12 fm is small, as expected for a light nucleus with a neutron excess of only 1. This result thus serves as a successful benchmark for electroweak determinations of neutron radii on heavier nuclei. A tree-level approach was used to extract the ^{27}Al weak radius R_{w}=3.00±0.15 fm, and the weak skin thickness R_{wk}-R_{ch}=-0.04±0.15 fm. The weak form factor at this Q^{2} is F_{wk}=0.39±0.04.

Unique Access to u-Channel Physics: Exclusive Backward-Angle Omega Meson Electroproduction.

Backward-angle meson electroproduction above the resonance region, which was previously ignored, is anticipated to offer unique access to the three quark plus sea component of the nucleon wave function. In this Letter, we present the first complete separation of the four electromagnetic structure functions above the resonance region in exclusive ω electroproduction off the proton, ep→e^{'}pω, at central Q^{2} values of 1.60, 2.45 GeV^{2}, at W=2.21 GeV. The results of our pioneering -u≈-u_{min} study demonstrate the existence of a unanticipated backward-angle cross section peak and the feasibility of full L/T/LT/TT separations in this never explored kinematic territory. At Q^{2}=2.45 GeV^{2}, the observed dominance of σ_{T} over σ_{L}, is qualitatively consistent with the collinear QCD description in the near-backward regime, in which the scattering amplitude factorizes into a hard subprocess amplitude and baryon to meson transition distribution amplitudes: universal nonperturbative objects only accessible through backward-angle kinematics.

JLab Measurements of the

The charge and magnetic form factors, F_{C} and F_{M}, respectively, of ^{3}He are extracted in the kinematic range 25 fm^{-2}≤Q^{2}≤61 fm^{-2} from elastic electron scattering by detecting ^{3}He recoil nuclei and scattered electrons in coincidence with the two High Resolution Spectrometers of the Hall A Facility at Jefferson Lab. The measurements find evidence for the existence of a second diffraction minimum for the magnetic form factor at Q^{2}=49.3 fm^{-2} and for the charge form factor at Q^{2}=62.0 fm^{-2}. Both minima are predicted to exist in the Q^{2} range accessible by this Jefferson Lab experiment. The data are in qualitative agreement with theoretical calculations based on realistic interactions and accurate methods to solve the three-body nuclear problem.

Publisher's Note: JLab Measurements of the

This corrects the article DOI: 10.1103/PhysRevLett.119.162501.

Polarization Transfer in Wide-Angle Compton Scattering and Single-Pion Photoproduction from the Proton.

Wide-angle exclusive Compton scattering and single-pion photoproduction from the proton have been investigated via measurement of the polarization transfer from a circularly polarized photon beam to the recoil proton. The wide-angle Compton scattering polarization transfer was analyzed at an incident photon energy of 3.7 GeV at a proton scattering angle of θ_{cm}^{p}=70°. The longitudinal transfer K_{LL}, measured to be 0.645±0.059±0.048, where the first error is statistical and the second is systematic, has the same sign as predicted for the reaction mechanism in which the photon interacts with a single quark carrying the spin of the proton. However, the observed value is ~3 times larger than predicted by the generalized-parton-distribution-based calculations, which indicates a significant unknown contribution to the scattering amplitude.

JLab measurement of the 4He charge form factor at large momentum transfers.

The charge form factor of 4He has been extracted in the range 29 fm(-2) ≤ Q2 ≤ 77 fm(-2) from elastic electron scattering, detecting 4He recoil nuclei and electrons in coincidence with the high resolution spectrometers of the Hall A Facility of Jefferson Lab. The measurements have uncovered a second diffraction minimum for the form factor, which was predicted in the Q2 range of this experiment. The data are in qualitative agreement with theoretical calculations based on realistic interactions and accurate methods to solve the few-body problem.

New measurements of high-momentum nucleons and short-range structures in nuclei.

We present new measurements of electron scattering from high-momentum nucleons in nuclei. These data allow an improved determination of the strength of two-nucleon correlations for several nuclei, including light nuclei where clustering effects can, for the first time, be examined. The data also include the kinematic region where three-nucleon correlations are expected to dominate.

Precise extraction of the induced polarization in the 4He(e,e'p)3H reaction.

We measured with unprecedented precision the induced polarization P(y) in (4)He(e,e'p)(3)H at Q(2)=0.8 and 1.3 (GeV/c)(2). The induced polarization is indicative of reaction-mechanism effects beyond the impulse approximation. Our results are in agreement with a relativistic distorted-wave impulse approximation calculation but are overestimated by a calculation with strong charge-exchange effects. Our data are used to constrain the strength of the spin-independent charge-exchange term in the latter calculation.

Scaling of the F2 structure function in nuclei and quark distributions at x>1.

We present new data on electron scattering from a range of nuclei taken in Hall C at Jefferson Lab. For heavy nuclei, we observe a rapid falloff in the cross section for x>1, which is sensitive to short-range contributions to the nuclear wave function, and in deep inelastic scattering corresponds to probing extremely high momentum quarks. This result agrees with higher energy muon scattering measurements, but is in sharp contrast to neutrino scattering measurements which suggested a dramatic enhancement in the distribution of the "superfast" quarks probed at x>1. The falloff at x>1 is noticeably stronger in 2H and 3He, but nearly identical for all heavier nuclei.

Probing quark-gluon interactions with transverse polarized scattering.

We have extracted QCD matrix elements from our data on doubly polarized inelastic scattering of electrons on nuclei. We find the higher twist matrix element d˜2, which arises strictly from quark-gluon interactions, to be unambiguously nonzero. The data also reveal an isospin dependence of higher twist effects if we assume that the Burkhardt-Cottingham sum rule is valid. The fundamental Bjorken sum rule obtained from the a0 matrix element is satisfied at our low momentum transfer.

Polarization transfer in the 4He(e,e'p)3H reaction at Q2=0.8 and 1.3 (GeV/c)2.

Proton recoil polarization was measured in the quasielastic 4He(e,e'p)3H reaction at Q{2}=0.8 and 1.3 (GeV/c){2} with unprecedented precision. The polarization-transfer coefficients are found to differ from those of the 1H(e,e'p) reaction, contradicting a relativistic distorted-wave approximation and favoring either the inclusion of medium-modified proton form factors predicted by the quark-meson coupling model or a spin-dependent charge-exchange final-state interaction. For the first time, the polarization-transfer ratio is studied as a function of the virtuality of the proton.

New measurements of the European Muon Collaboration effect in very light nuclei.

New Jefferson Lab data are presented on the nuclear dependence of the inclusive cross section from (2)H, (3)He, (4)He, (9)Be and (12)C for 0.3 < x < 0.9, Q(2) approximately 3-6 GeV(2). These data represent the first measurement of the EMC effect for (3)He at large x and a significant improvement for (4)He. The data do not support previous A-dependent or density-dependent fits to the EMC effect and suggest that the nuclear dependence of the quark distributions may depend on the local nuclear environment.

Probing cold dense nuclear matter.

The protons and neutrons in a nucleus can form strongly correlated nucleon pairs. Scattering experiments, in which a proton is knocked out of the nucleus with high-momentum transfer and high missing momentum, show that in carbon-12 the neutron-proton pairs are nearly 20 times as prevalent as proton-proton pairs and, by inference, neutron-neutron pairs. This difference between the types of pairs is due to the nature of the strong force and has implications for understanding cold dense nuclear systems such as neutron stars.

Measurements of the proton elastic-form-factor ratio mu pG p E/G p M at low momentum transfer.

High-precision measurements of the proton elastic form-factor ratio, mu pG p E/G p M, have been made at four-momentum transfer, Q2, values between 0.2 and 0.5 GeV2. The new data, while consistent with previous results, clearly show a ratio less than unity and significant differences from the central values of several recent phenomenological fits. By combining the new form-factor ratio data with an existing cross-section measurement, one finds that in this Q2 range the deviation from unity is primarily due to G p E being smaller than expected.

Measurement of nuclear transparency for the A(e,e'pi+) reaction.

We have measured the nuclear transparency of the A(e,e'pi+) process in 2H, 12C, 27Al, 63Cu, and 197Au targets. These measurements were performed at the Jefferson Laboratory over a four momentum transfer squared range Q2=1.1 to 4.7 (GeV/c)2. The nuclear transparency was extracted as the super-ratio of (sigmaA/sigmaH) from data to a model of pion-electroproduction from nuclei without pi-N final-state interactions. The Q2 and atomic number dependence of the nuclear transparency both show deviations from traditional nuclear physics expectations and are consistent with calculations that include the quantum chromodynamical phenomenon of color transparency.

Investigation of proton-proton short-range correlations via the 12C(e,e'pp) reaction.

We investigated simultaneously the 12C(e,e'p) and 12C(e,e'pp) reactions at Q2=2 (GeV/c)2, xB=1.2, and in an (e, e'p) missing-momentum range from 300 to 600 MeV/c. At these kinematics, with a missing momentum greater than the Fermi momentum of nucleons in a nucleus and far from the delta excitation, short-range nucleon-nucleon correlations are predicted to dominate the reaction. For (9.5+/-2)% of the 12C(e,e'p) events, a recoiling partner proton was observed back-to-back to the 12C(e,e'p) missing-momentum vector, an experimental signature of correlations.

Proton spin structure in the resonance region.

We have examined the spin structure of the proton in the region of the nucleon resonances (1.085 GeV

Longitudinal-transverse separations of deep-inelastic structure functions at low Q2 for hydrogen and deuterium.

We report on a study of the longitudinal to transverse cross section ratio, R=sigmaL/sigmaT, at low values of x and Q2, as determined from inclusive inelastic electron-hydrogen and electron-deuterium scattering data from Jefferson Laboratory Hall C spanning the four-momentum transfer range 0.06