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.

A glimpse of gluons through deeply virtual compton scattering on the proton.

The internal structure of nucleons (protons and neutrons) remains one of the greatest outstanding problems in modern nuclear physics. By scattering high-energy electrons off a proton we are able to resolve its fundamental constituents and probe their momenta and positions. Here we investigate the dynamics of quarks and gluons inside nucleons using deeply virtual Compton scattering (DVCS)-a highly virtual photon scatters off the proton, which subsequently radiates a photon. DVCS interferes with the Bethe-Heitler (BH) process, where the photon is emitted by the electron rather than the proton. We report herein the full determination of the BH-DVCS interference by exploiting the distinct energy dependences of the DVCS and BH amplitudes. In the regime where the scattering is expected to occur off a single quark, measurements show an intriguing sensitivity to gluons, the carriers of the strong interaction.

Rosenbluth Separation of the π

We report the first longitudinal-transverse separation of the deeply virtual exclusive π^{0} electroproduction cross section off the neutron and coherent deuteron. The corresponding four structure functions dσ_{L}/dt, dσ_{T}/dt, dσ_{LT}/dt, and dσ_{TT}/dt are extracted as a function of the momentum transfer to the recoil system at Q^{2}=1.75 GeV^{2} and x_{B}=0.36. The ed→edπ^{0} cross sections are found compatible with the small values expected from theoretical models. The en→enπ^{0} cross sections show a dominance from the response to transversely polarized photons, and are in good agreement with calculations based on the transversity generalized parton distributions of the nucleon. By combining these results with previous measurements of π^{0} electroproduction off the proton, we present a flavor decomposition of the u and d quark contributions to the cross section.

Rosenbluth Separation of the π

We present deeply virtual π^{0} electroproduction cross-section measurements at x_{B}=0.36 and three different Q^{2} values ranging from 1.5 to 2 GeV^{2}, obtained from Jefferson Lab Hall A experiment E07-007. The Rosenbluth technique is used to separate the longitudinal and transverse responses. Results demonstrate that the cross section is dominated by its transverse component and, thus, is far from the asymptotic limit predicted by perturbative quantum chromodynamics. Nonetheless, an indication of a nonzero longitudinal contribution is provided by the measured interference term σ_{LT}. Results are compared with several models based on the leading-twist approach of generalized parton distributions (GPDs). In particular, a fair agreement is obtained with models in which the scattering amplitude includes convolution terms of chiral-odd (transversity) GPDs of the nucleon with the twist-3 pion distribution amplitude. This experiment, together with previous extensive unseparated measurements, provides strong support to the exciting idea that transversity GPDs can be accessed via neutral pion electroproduction in the high-Q^{2} regime.

Measurement of the Target-Normal Single-Spin Asymmetry in Quasielastic Scattering from the Reaction (3)He(↑)(e,e').

We report the first measurement of the target single-spin asymmetry, A(y), in quasielastic scattering from the inclusive reaction (3)He(↑)(e,e') on a (3)He gas target polarized normal to the lepton scattering plane. Assuming time-reversal invariance, this asymmetry is strictly zero for one-photon exchange. A nonzero A(y) can arise from the interference between the one- and two-photon exchange processes which is sensitive to the details of the substructure of the nucleon. An experiment recently completed at Jefferson Lab yielded asymmetries with high statistical precision at Q(2)=0.13, 0.46, and 0.97 GeV(2). These measurements demonstrate, for the first time, that the (3)He asymmetry is clearly nonzero and negative at the 4σ-9σ level. Using measured proton-to-(3)He cross-section ratios and the effective polarization approximation, neutron asymmetries of -(1-3)% were obtained. The neutron asymmetry at high Q(2) is related to moments of the generalized parton distributions (GPDs). Our measured neutron asymmetry at Q(2)=0.97 GeV(2) agrees well with a prediction based on two-photon exchange using a GPD model and thus provides a new, independent constraint on these distributions.

Measurement of double-polarization asymmetries in the quasielastic (3)He[→](e[→],e(')d) process.

We present a precise measurement of double-polarization asymmetries in the ^{3}He[over →](e[over →],e^{'}d) reaction. This particular process is a uniquely sensitive probe of hadron dynamics in ^{3}He and the structure of the underlying electromagnetic currents. The measurements have been performed in and around quasielastic kinematics at Q^{2}=0.25(GeV/c)^{2} for missing momenta up to 270 MeV/c. The asymmetries are in fair agreement with the state-of-the-art calculations in terms of their functional dependencies on p_{m} and ω, but are systematically offset. Beyond the region of the quasielastic peak, the discrepancies become even more pronounced. Thus, our measurements have been able to reveal deficiencies in the most sophisticated calculations of the three-body nuclear system, and indicate that further refinement in the treatment of their two-and/or three-body dynamics is required.

Precision measurement of the neutron twist-3 matrix element d(2)(n): probing color forces.

Double-spin asymmetries and absolute cross sections were measured at large Bjorken x (0.25≤x≤0.90), in both the deep-inelastic and resonance regions, by scattering longitudinally polarized electrons at beam energies of 4.7 and 5.9 GeV from a transversely and longitudinally polarized (3)He target. In this dedicated experiment, the spin structure function g(2)((3)He) was determined with precision at large x, and the neutron twist-3 matrix element d(2)(n) was measured at ⟨Q(2)⟩ of 3.21 and 4.32 GeV(2)/c(2), with an absolute precision of about 10(-5). Our results are found to be in agreement with lattice QCD calculations and resolve the disagreement found with previous data at ⟨Q(2)⟩=5 GeV(2)/c(2). Combining d(2)(n) and a newly extracted twist-4 matrix element f(2)(n), the average neutron color electric and magnetic forces were extracted and found to be of opposite sign and about 30 MeV/fm in magnitude.

Measurement of the target-normal single-spin asymmetry in deep-inelastic scattering from the reaction (3)He(↑)(e,e')X.

We report the first measurement of the target-normal single-spin asymmetry in deep-inelastic scattering from the inclusive reaction 3)He(↑)(e,e')X on a polarized (3)He gas target. Assuming time-reversal invariance, this asymmetry is strictly zero in the Born approximation but can be nonzero if two-photon-exchange contributions are included. The experiment, conducted at Jefferson Lab using a 5.89 GeV electron beam, covers a range of 1.72 GeV, which is nonzero at the 2.89σ level. Our measured asymmetry agrees both in sign and magnitude with a two-photon-exchange model prediction that uses input from the Sivers transverse momentum distribution obtained from semi-inclusive deep-inelastic scattering.

Beam-target double-spin asymmetry A{LT} in charged pion production from deep inelastic scattering on a transversely polarized {3}He target at 1.4

We report the first measurement of the double-spin asymmetry A{LT} for charged pion electroproduction in semi-inclusive deep-inelastic electron scattering on a transversely polarized {3}He target. The kinematics focused on the valence quark region, 0.16

Single spin asymmetries in charged pion production from semi-inclusive deep inelastic scattering on a transversely polarized 3He Target at Q2 = 1.4-2.7 GeV2.

We report the first measurement of target single spin asymmetries in the semi-inclusive (3)He(e,e'π(±))X reaction on a transversely polarized target. The experiment, conducted at Jefferson Lab using a 5.9 GeV electron beam, covers a range of 0.16 < x < 0.35 with 1.4 < Q(2) < 2.7 GeV(2). The Collins and Sivers moments were extracted from the azimuthal angular dependence of the measured asymmetries. The π(±) Collins moments for (3)He are consistent with zero, except for the π(+) moment at x = 0.35, which deviates from zero by 2.3σ. While the π(-) Sivers moments are consistent with zero, the π(+) Sivers moments favor negative values. The neutron results were extracted using the nucleon effective polarization and measured cross section ratios of proton to (3)He, and are largely consistent with the predictions of phenomenological fits and quark model calculations.

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.

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.

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.

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.