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The neutron is a cornerstone in our depiction of the visible universe. Despite the neutron zero-net electric charge, the asymmetric distribution of the positively- (up) and negatively-charged (down) quarks, a result of the complex quark-gluon dynamics, lead to a negative value for its squared charge radius, ⟨ r n 2 ⟩ . The precise measurement of the neutron’s charge radius thus emerges as an essential part of unraveling its structure. Here we report on a ⟨ r n 2 ⟩ measurement, based on the extraction of the neutron electric form factor, G E n , at low four-momentum transfer squared ( Q 2 ) by exploiting the long known connection between the N  → Δ quadrupole transitions and the neutron electric form factor. Our result, ⟨ r n 2 ⟩ = − 0.110 ± 0.008 ( fm 2 ) , addresses long standing unresolved discrepancies in the ⟨ r n 2 ⟩ determination. The dynamics of the strong nuclear force can be viewed through the precise picture of the neutron’s constituent distributions that result into the non-zero ⟨ r n 2 ⟩ value. The charge radius of nucleons provides information about their structure. Here the authors present a method, based values of neutron electric form factors, to determine the charge radius of the neutron and provide information on improving the uncertainty of neutron charge radius measurements

The proton is one of the main building blocks of all visible matter in the Universe 1 . Among its intrinsic properties are its electric charge, mass and spin 2 . These properties emerge from the complex dynamics of its fundamental constituents—quarks and gluons—described by the theory of quantum chromodynamics 3 – 5 . The electric charge and spin of protons, which are shared among the quarks, have been investigated previously using electron scattering 2 . An example is the highly precise measurement of the electric charge radius of the proton 6 . 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 proton 7 , 8  from our measurement. We used a variety of models 9 – 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 chromodynamics 12 . This work paves the way for a deeper understanding of the salient role of gluons in providing gravitational mass to visible matter. The gluonic gravitational form factor of the proton was determined using various models, and these analyses showed that the mass radius of the proton was smaller than the electric charge radius.

The visible world is founded on the proton, the only composite building block of matter that is stable in nature. Consequently, understanding the formation of matter relies on explaining the dynamics and the properties of the proton’s bound state. A fundamental property of the proton involves the response of the system to an external electromagnetic field. It is characterized by the electromagnetic polarizabilities 1 that describe how easily the charge and magnetization distributions inside the system are distorted by the electromagnetic field. Moreover, the generalized polarizabilities 2 map out the resulting deformation of the densities in a proton subject to an electromagnetic field. They disclose essential information about the underlying system dynamics and provide a key for decoding the proton structure in terms of the theory of the strong interaction that binds its elementary quark and gluon constituents. Of particular interest is a puzzle in the electric generalized polarizability of the proton that remains unresolved for two decades 2 . Here we report measurements of the proton’s electromagnetic generalized polarizabilities at low four-momentum transfer squared. We show evidence of an anomaly to the behaviour of the proton’s electric generalized polarizability that contradicts the predictions of nuclear theory and derive its signature in the spatial distribution of the induced polarization in the proton. The reported measurements suggest the presence of a new, not-yet-understood dynamical mechanism in the proton and present notable challenges to the nuclear theory. Measurements of the proton’s electromagnetic structure show enhancement of its electric generalized polarizability compared with theoretical expectations, confirming the presence of a new dynamical mechanism not accounted for by current theories.

The MUSE experiment at the Paul Scherrer Institute is measuring elastic lepton-proton scattering cross sections in a four-momentum transfer range from Q 2 of approximately 0.002–0.08 GeV 2 using positively and negatively charged electrons and muons. The extraction of the Born cross sections from the experimental data requires radiative corrections. Estimates of the instrumental uncertainties in those corrections have been made using the ESEPP event generator. The results depend in particular on the minimum lepton momentum that contributes to the experimental cross section and the fraction of events with hard initial-state radiation that is detected in the MUSE calorimeter and is excluded from the data. These results show that the angular-dependent instrumental uncertainties in radiative corrections to the electron cross section are less than 0.4% and are negligible for the muon cross section.

The MUSE experiment at the Paul Scherrer Institute is measuring elastic lepton-proton scattering cross sections in a four-momentum transfer range from Q2 of approximately 0.002–0.08 GeV2 using positively and negatively charged electrons and muons. The extraction of the Born cross sections from the experimental data requires radiative corrections. Estimates of the instrumental uncertainties in those corrections have been made using the ESEPP event generator. The results depend in particular on the minimum lepton momentum that contributes to the experimental cross section and the fraction of events with hard initial-state radiation that is detected in the MUSE calorimeter and is excluded from the data. Furthermore, these results show that the angular-dependent instrumental uncertainties in radiative corrections to the electron cross section are less than 0.4% and are negligible for the muon cross section.

The proton is one of the main building blocks of all visible matter in the universe. Among its intrinsic properties are its electric charge, mass, and spin. These emerge from the complex dynamics of its fundamental constituents, quarks and gluons, described by the theory of quantum chromodynamics (QCD). Using electron scattering its electric charge and spin, shared among the quark constituents, have been the topic of active investigation until today. An example is the novel precision measurement of the proton's electric charge radius. In contrast, little is known about the proton's inner mass density, dominated by the energy carried by the gluons, which are hard to access through electron scattering since gluons carry no electromagnetic charge. In the present work we chose to probe this gluonic gravitational density using a small color dipole, theJ/ψparticle, through its threshold photoproduction. From our data we determined, for the first time, the proton's gluonic gravitational form factors, which encode its mass density. We used a variety of methods and determined in all cases a mass radius that is notably smaller than the electric charge radius. In some cases, the determined radius is in excellent agreement with first-principle predictions from lattice QCD. This work paves the way for a deeper understanding of the salient role of gluons in providing gravitational mass to visible matter.

Here, we report new pion electroproduction measurements in the Δ (1232) resonance, utilizing the SHMS - HMS magnetic spectrometers of Hall C at Jefferson Lab. The data focus on a region that exhibits a strong and rapidly changing interplay of the mesonic cloud and quark-gluon dynamics in the nucleon. The results are in reasonable agreement with models that employ pion cloud effects and chiral effective field theory calculations, but at the same time they suggest that an improvement is required to the theoretical calculations and provide valuable input that will allow their refinements. The data illustrate the potential of the magnetic spectrometers setup in Hall C towards the study the Δ (1232) resonance. These first reported results will be followed by a series of measurements in Hall C, that will expand the studies of the Δ (1232) resonance offering a high precision insight within a wide kinematic range from low to high momentum transfers.

We report new pion electroproduction measurements in the Δ ( 1232 ) resonance, utilizing the SHMS - HMS magnetic spectrometers of Hall C at Jefferson Lab. The data focus on a region that exhibits a strong and rapidly changing interplay of the mesonic cloud and quark-gluon dynamics in the nucleon. The results are in reasonable agreement with models that employ pion cloud effects and chiral effective field theory calculations, but at the same time they suggest that an improvement is required to the theoretical calculations and provide valuable input that will allow their refinements. The data illustrate the potential of the magnetic spectrometers setup in Hall C towards the study the Δ ( 1232 ) resonance. These first reported results will be followed by a series of measurements in Hall C, that will expand the studies of the Δ ( 1232 ) resonance offering a high precision insight within a wide kinematic range from low to high momentum transfers.

This review gives an update on virtual Compton scattering (VCS) off the nucleon, \\(\\gamma^* N \\to N \\gamma\\), in the low-energy regime. We recall the theoretical formalism related to the generalized polarizabilities (GPs) and model predictions for these observables. We present the GP extraction methods that are used in the experiments: the approach based on the low-energy theorem for VCS and the formalism of Dispersion Relations. We then review the experimental results, with a focus on the progress brought by recent experimental data on proton generalized polarizabilities, and we conclude by some perspectives in the field of VCS at low energy.