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Measuring the spin structure of protons and neutrons tests our understanding of how they arise from quarks and gluons, the fundamental building blocks of nuclear matter. At long distances, the coupling constant of the strong interaction becomes large, requiring non-perturbative methods to calculate quantum chromodynamics processes, such as lattice gauge theory or effective field theories. Here we report proton spin structure measurements from scattering a polarized electron beam off polarized protons. The spin-dependent cross-sections were measured at large distances, corresponding to the region of low momentum transfer squared between 0.012 and 1.0 GeV2. This kinematic range provides unique tests of chiral effective field theory predictions. Our results show that a complete description of the nucleon spin remains elusive, and call for further theoretical works, for example, in lattice quantum chromodynamics. Finally, our data extrapolated to the photon point agree with the Gerasimov–Drell–Hearn sum rule, a fundamental prediction of quantum field theory that relates the anomalous magnetic moment of the proton to its integrated spin-dependent cross-sections.Measurements of the proton’s spin structure in experiments scattering a polarized electron beam off polarized protons in regions of low momentum transfer squared test predictions from chiral effective field theory of the strong interaction.

We review recent theoretical and experimental progress on the role of two-photon exchange (TPE) in electron-proton scattering at low to moderate momentum transfers. We make a detailed comparison and analysis of the results of competing experiments on the ratio of e+p to e-p elastic scattering cross sections, and of the theoretical calculations describing them. A summary of the current experimental situation is provided, along with an outlook for future experiments.

We report the first measurements of deep inelastic scattering spin-dependent azimuthal asymmetries in back-to-back dihadron electroproduction, where two hadrons are produced in opposite hemispheres along the z-axis in the center-of-mass frame, with the first hadron produced in the current-fragmentation region and the second in the target-fragmentation region. The data were taken with longitudinally polarized electron beams of 10.2 and 10.6 GeV incident on an unpolarized liquid-hydrogen target using the CLAS12 spectrometer at Jefferson Lab. Observed non-zero \\(\\sin\\Delta\\phi\\) modulations in \\(ep \\rightarrow e'p\\pi^+X\\) events, where \\(\\Delta\\phi\\) is the difference of the azimuthal angles of the proton and pion in the virtual photon and target nucleon center-of-mass frame, indicate that correlations between the spin and transverse momenta of hadrons produced in the target- and current-fragmentation regions may be significant. The measured beam-spin asymmetries provide a first access in dihadron production to a previously unobserved leading-twist spin- and transverse-momentum-dependent fracture function. The fracture functions describe the hadronization of the target remnant after the hard scattering of a virtual photon off a quark in the target particle and provide a new avenue for studying nucleonic structure and hadronization.

The polarized cross section ratio \\(\\sigma_{LT'}/\\sigma_{0}\\) from hard exclusive \\(\\pi^{-} \\Delta^{++}\\) electroproduction off an unpolarized hydrogen target has been extracted based on beam-spin asymmetry measurements using a 10.2 GeV / 10.6 GeV incident electron beam and the CLAS12 spectrometer at Jefferson Lab. The study, which provides the first observation of this channel in the deep-inelastic regime, focuses on very forward-pion kinematics in the valence regime, and photon virtualities ranging from 1.5 GeV\\(^{2}\\) up to 7 GeV\\(^{2}\\). The reaction provides a novel access to the \\(d\\)-quark content of the nucleon and to \\(p \\rightarrow \\Delta^{++}\\) transition generalized parton distributions. A comparison to existing results for hard exclusive \\(\\pi^{+} n\\) and \\(\\pi^{0} p\\) electroproduction is provided, which shows a clear impact of the excitation mechanism, encoded in transition generalized parton distributions, on the asymmetry.

We report results of \\(\\Lambda\\) hyperon production in semi-inclusive deep-inelastic scattering off deuterium, carbon, iron, and lead targets obtained with the CLAS detector and the Continuous Electron Beam Accelerator Facility 5.014~GeV electron beam. These results represent the first measurements of the \\(\\Lambda\\) multiplicity ratio and transverse momentum broadening as a function of the energy fraction~(\\(z\\)) in the current and target fragmentation regions. The multiplicity ratio exhibits a strong suppression at high~\\(z\\)~and~an enhancement at~low~\\(z\\). The measured transverse momentum broadening is an order of magnitude greater than that seen for light mesons. This indicates that the propagating entity interacts very strongly with the nuclear medium, which suggests that propagation of diquark configurations in the nuclear medium takes place at least part of the time, even at high~\\(z\\). The trends of these results are qualitatively described by the Giessen Boltzmann-Uehling-Uhlenbeck transport model, particularly for the multiplicity ratios. These observations will potentially open a new era of studies of the structure of the nucleon as well as of strange baryons.

Beam-recoil transferred polarizations for the exclusive electroproduction of \\(K^+\\Lambda\\) and \\(K^+\\Sigma^0\\) final states from an unpolarized proton target have been measured using the CLAS12 spectrometer at Jefferson Laboratory. The measurements at beam energies of 6.535~GeV and 7.546~GeV span the range of four-momentum transfer \\(Q^2\\) from 0.3 to 4.5~GeV\\(^2\\) and invariant energy \\(W\\) from 1.6 to 2.4~GeV, while covering the full center-of-mass angular range of the \\(K^+\\). These new data extend the existing hyperon polarization data from CLAS in a similar kinematic range but from a significantly larger dataset. They represent an important addition to the world data, allowing for better exploration of the reaction mechanism in strangeness production processes, for further understanding of the spectrum and structure of excited nucleon states, and for improved insight into the strong interaction in the regime of non-perturbative dynamics.

We measured the \\(g_1\\) spin structure function of the deuteron at low \\(Q^{2}\\), where QCD can be approximated with chiral perturbation theory (\\(\\chi\\)PT). The data cover the resonance region, up to an invariant mass of \\(W\\approx1.9\\)~GeV. The generalized Gerasimov-Drell-Hearn sum, the moment \\(\\bar{\\Gamma}_{1}^{d}\\) and the integral \\(\\bar{I}_\\gamma^d\\) related to the spin polarizability \\(\\gamma_{0}^{d}\\) are precisely determined down to a minimum \\(Q^2\\) of 0.02~GeV\\(^2\\) for the first time, about 2.5 times lower than that of previous data. We compare them to several \\(\\chi\\)PT calculations and models. These results are the first in a program of benchmark measurements of polarization observables in the \\(\\chi\\)PT domain.

High precision measurements of the polarized electron beam-spin asymmetry in semi-inclusive deep inelastic scattering (SIDIS) from the proton have been performed using a 10.6~GeV incident electron beam and the CLAS12 spectrometer at Jefferson Lab. We report here a high precision multidimensional study of single \\(\\pi^{+}\\) SIDIS data over a large kinematic range in Bjorken x, fractional energy and transverse momentum of the hadron as well as photon virtualities \\(Q^{2}\\) ranging from \\(1-7\\,\\)GeV\\(^{2}\\). In particular, the structure function ratio \\(F^{\\sin\\phi}_{LU}/F_{UU}\\) has been determined, where \\(F^{\\sin\\phi}_{LU}\\) is a twist-3 quantity that can reveal novel aspects of emergent hadron mass and quark-gluon correlations within the nucleon. The data's impact on the evolving understanding of the underlying reaction mechanisms and their kinematic variation is explored using theoretical models for the different contributing transverse momentum dependent parton distribution functions.

The first results on the \\(\\sigma_{LT'}\\) structure function in exclusive \\(\\pi^0p\\) electroproduction at invariant masses of the final state of 1.5 GeV \\(<\\) \\(W\\) \\(<\\) 1.8 GeV and in the range of photon virtualities 0.4 GeV\\(^2 < Q^2 < 1.0\\) GeV\\(^2\\) were obtained from data on beam spin asymmetries and differential cross sections measured with the CLAS detector at Jefferson Lab. The Legendre moments determined from the \\(\\sigma_{LT'}\\) structure function have demonstrated sensitivity to the contributions from the nucleon resonances in the second and third resonance regions. These new data on the beam spin asymmetries in \\(\\pi^0p\\) electroproduction extend the opportunities for the extraction of the nucleon resonance electroexcitation amplitudes in the mass range above 1.6 GeV.

We report measurements of the exclusive electroproduction of \\(K^+\\Lambda\\) and \\(K^+\\Sigma^0\\) final states from an unpolarized proton target using the CLAS detector at the Thomas Jefferson National Accelerator Facility. The separated structure functions \\(\\sigma_U\\), \\(\\sigma_{LT}\\), \\(\\sigma_{TT}\\), and \\(\\sigma_{LT'}\\) were extracted from the \\(\\Phi\\)-dependent differential cross sections acquired with a longitudinally polarized 5.499 GeV electron beam. The data span a broad range of momentum transfers \\(Q^2\\) from 1.4 to 3.9 GeV\\(^2\\), invariant energy \\(W\\) from threshold to 2.6 GeV, and nearly the full center-of-mass angular range of the kaon. The separated structure functions provide an unprecedented data sample, which in conjunction with other meson photo- and electroproduction data, will help to constrain the higher-level analyses being performed to search for missing baryon resonances.