We review the dispersion-theoretical analysis of the electromagnetic form factors of the nucleon. We emphasize in particular the role of unitarity and analyticity in the construction of the isoscalar and isovector spectral functions. We present new results on the extraction of the nucleon radii, the electric and magnetic form factors and the extraction of $ω$-meson couplings. All this is supplemented by a detailed calculation of the theoretical uncertainties, using bootstrap and Bayesian methods to pin down the statistical errors, while systematic errors are determined from variations of the spectral functions. We also discuss the physics of the time-like form factors and point out further issues to be addressed in this framework.
In Poincaré-covariant continuum treatments of the three valence-quark bound-state problem, the force behind dynamical chiral symmetry breaking also generates nonpointlike, interacting diquark correlations in the nucleon and its resonances. We detail the impact of these correlations on the electromagnetically-induced nucleon-$Δ$ and nucleon-Roper transitions, providing a flavour-separation of the latter and associated predictions that can be tested at modern facilities.
We compute the electromagnetic form factors of the nucleon in the Poincare-covariant Faddeev framework based on the Dyson-Schwinger equations of QCD. The general expression for a baryon's electromagnetic current in terms of three interacting dressed quarks is derived. Upon employing a rainbow-ladder gluon-exchange kernel for the quark-quark interaction, the nucleon's Faddeev amplitude and electromagnetic form factors are computed without any further truncations or model assumptions. The form factor results show clear evidence of missing pion-cloud effects below a photon momentum transfer of ~2…
Elastic electromagnetic nucleon form factors have long provided vital information about the structure and composition of these most basic elements of nuclear physics. The form factors are a measurable and physical manifestation of the nature of the nucleons' constituents and the dynamics that binds them together. Accurate form factor data obtained in recent years using modern experimental facilities has spurred a significant reevaluation of the nucleon and pictures of its structure; e.g., the role of quark orbital angular momentum, the scale at which perturbative QCD effects should become evid…
The electromagnetic form factors of the proton and the neutron in the timelike region are reviewed. In view of the forthcoming experimental projects devoted to investigate these observables, we present the current status of the field and we emphasize the relevant role, that accurate measurements, refined phenomenological analyses, as well as microscopic models will play with the goal of achieving deeper insights into the structure of the nucleon and its inner dynamics.
The effects of charge symmetry breaking in nucleon electromagnetic form factors on parity- violating elastic electron-12C scattering is studied, and found to be much smaller than other known effects. The analysis of a planned experiment is discussed.
Recent measurements of nucleon resonance transition form factors with CLAS at Jefferson Lab are discussed. The new data resolve a long-standing puzzle of the nature of the Roper resonance, and confirm the assertion of the symmetric constituent quark model of the Roper as the first radial excitation of the nucleon. The data on $nπ^+$ production at high $Q^2$ confirm the slow fall off of the $S_{11}(1535)$ transition form factor with $Q^2$, and better constrain the branching ratios $β_{Nπ}=0.50$ and $β_{Nη}=0.45$. Also, new results on the transition amplitudes for the $D_{13}(1520)$ resonance ar…
We present results on the nucleon electromagnetic form factors within lattice QCD using two flavors of degenerate twisted mass fermions. Volume effects are examined using simulations at two volumes of spatial length L=2.1 fm and L=2.8 fm. Cut-off effects are investigated using three different values of the lattice spacings, namely a=0.089 fm, a=0.070 and a=0.056 fm. The nucleon magnetic moment, Dirac and Pauli radii are obtained in the continuum limit and chirally extrapolated to the physical pion mass allowing for a comparison with experiment.
We compute the electromagnetic form factors of the nucleon in quenched lattice QCD, using non-perturbatively improved Wilson fermions, and compare the results with phenomenology and chiral effective field theory.
We investigate the electromagnetic form factors of nucleons within a simple relativistic quark spectator-diquark model using the light-cone formalism. Melosh rotations are applied to both quark and vector diquark. It is shown that the difference between vector and scalar spectator diquarks reproduces the right electric form factor of neutrons, and both the form factors $G_E(Q^2)$ and $G_M(Q^2)$ of the proton and neutron agree with experimental data well up to $Q^2=2 ~\rm{GeV}^2$ in this simple model.
In Poincaré-covariant continuum treatments of the three valence-quark bound-state problem, the force behind dynamical chiral symmetry breaking also generates nonpointlike, interacting diquark correlations in the nucleon and its resonances. We detail the impact of these correlations on the nucleon's elastic and nucleon-to-Roper transition electromagnetic form factors, providing flavour-separation versions that can be tested at modern facilities.
The study of nucleon resonances in electromagnetic meson production with the CLAS detector is discussed. The electromagnetic interaction is complementary to pion scattering in the exploration of the nucleon excitation spectrum. Higher mass states often decouple from the $Nπ$ channel and are not seen in $πN \to πN$. Photoproduction of mesons, such as $KΛ$, $ωp$ and $η^\prime p$ may be more sensitive to many of these states. The CLAS detector, combined with the use of energy-tagged polarized photons and polarized electrons, as well as polarized targets and the measurement of recoil polarization,…
We calculate the electromagnetic form factors of the nucleon within the light-cone sum rule approach. In comparison to previous work (hep-ph/0112085) we suggest to use a pure isospin-1/2 interpolating field for the nucleon, since the Chernyak-Zhitnitsky current leads to numerically large, unphysical, isospin violating contributions. The leading-order sum rules are derived for the form factors and the results are confronted with the experimental data. Our approach tends to favor the nucleon distribution amplitudes that are not far from the asymptotic shape.
Using baryon chiral perturbation theory including vector mesons, we analyse various continuum contributions to the isoscalar electromagnetic spectral functions of the nucleon induced by the leading order couplings.
Electron scattering at large Q^2 probes a nucleon's quark core. This core's contribution to electromagnetic form factors may be calculated using Poincare' covariant Faddeev amplitudes combined with a nucleon-photon vertex that automatically fulfills a Ward-Takahashi identity for on-shell nucleons. The calculated behaviour of G_E^p(Q^2)/G_M^p(Q^2) on 2<Q^2(GeV^2)<6 agrees with that inferred from polarisation transfer data, and exhibits a zero at Q^2\approx 6.5 GeV^2. There is some evidence that F_2(Q^2)/F_1(Q^2) \propto [\ln(Q^2/Λ^2)]^2/Q^2 for Q^2>6 GeV^2.
Impact of the in-medium modified nucleon weak and electromagnetic form factors on the neutrino mean free path in dense matter is studied by considering both the weak and electromagnetic interactions of neutrinos with the constituents of the matter. A relativistic mean field model and the quark-meson coupling model are respectively adopted for the in-medium effective nucleon mass and nucleon form factors. We find that the cross sections of neutrino scattering in cold nuclear medium decreases when the in-medium modification of the nucleon weak and electromagnetic form factors are taken into acco…
We apply the single quark transition model to resonance transition amplitudes extracted from photo-and electroproduction data. We use experimental data on the S11(1535) and D13(1520) nucleon resonances to extract the amplitudes for the electromagnetic transition from the nucleon ground state to the [70,1-] SU(6)xO(3) supermultiplet, and make predictions for the transition amplitudes of all other states associated with the [70,1-]. We find suprisingly good agreement with the data.
We utilize a light-front relativistic quark model (LF RQM) to predict the 3q core contribution to the electroexcitation amplitudes for the Delta(1232)P33, N(1440)P11, N(1520)D13, and N(1535)S11 up to Q2= 12GeV2. The parameters of the model have been specified via description of the nucleon electromagnetic form factors in the approach that combines 3q and pion-cloud contributions in the LF dynamics.
We reanalyze the world data on the electromagnetic form factors of the nucleon. The calculations are performed in the framework of an algebraic model of the nucleon combined with vector meson dominance.
We evaluate the isovector nucleon electromagnetic form factors in quenched and full QCD on the lattice using Wilson fermions. In the quenched theory we use a lattice of spatial size 3 fm at beta=6.0 enabling us to reach low momentum transfers and a lowest pion mass of about 400 MeV. In the full theory we use a lattice of spatial size 1.9 fm at beta=5.6 and lowest pion mass of about 380 MeV enabling comparison with the results obtained in the quenched theory. We compare our lattice results to the isovector part of the experimentally measured form factors.
External electromagnetic fields can provoke stress, and thus modifications of the internal structure of nucleons. Working with this hypothesis, one can derive a simple description of the charge dependence of the EMC effect. This first result is confirmed by two explicit models of the structure functions of deformed nucleons in the atomic nucleus. For large nuclei a continuous model is used. For small nuclei a discrete distribution of nuclear matter gives better results.
We compute corrections to both the isovector anomalous magnetic moment and the isovector electromagnetic current of the nucleon to $O(p^3)$ in the framework of covariant two-flavor Baryon Chiral Perturbation Theory. We then apply these corrections to lattice data for the anomalous magnetic moment from the LHPC, RBC & UKQCD and QCDSF collaborations.
Recent experimental data on space- and time-like form factors of the nucleon are analyzed in terms of a two-component model with a quark-like intrinsics structure and a meson cloud. A good overall agreement is found for all electromagnetic form factors with the exception of the neutron magnetic form factor in the time-like region.
We update the determination of the isovector nucleon electromagnetic self-energy, valid to leading order in QED. A technical oversight in the literature concerning the elastic contribution to Cottingham's formula is corrected and modern knowledge of the structure functions is used to precisely determine the inelastic contribution. We find δM_{p-n}^γ= 1.30(03)(47) MeV. The largest uncertainty arises from a subtraction term required in the dispersive analysis, which can be related to the isovector magnetic polarizability. With plausible model assumptions, we can combine our calculation with addi…
Longitudinal and transverse quark momentum distributions in the nucleon are calculated from a phenomenological quark-nucleon vertex function obtained through an investigation of the nucleon electromagnetic form factors within a light-front framework.
A Poincare' covariant Faddeev equation, which describes baryons as composites of confined-quarks and -nonpointlike-diquarks, is solved to obtain masses and Faddeev amplitudes for the nucleon and Delta. The amplitudes are a component of a nucleon-photon vertex that automatically fulfills the Ward-Takahashi identity for on-shell nucleons. These elements are sufficient for the calculation of a quark core contribution to the nucleons' electromagnetic form factors. An accurate description of the static properties is not possible with the core alone but the error is uniformly reduced by the incorpor…
The exact evaluation of the disconnected diagram contributions to the flavor-singlet pseudoscalar meson mass, the nucleon sigma term and the nucleon electromagnetic form factors, is carried out utilizing GPGPU technology with the NVIDIA CUDA platform. The disconnected loops are also computed using stochastic methods with several noise reduction techniques. Various dilution schemes as well as the truncated solver method are studied. We make a comparison of these stochastic techniques to the exact results and show that the number of noise vectors depends on the operator insertion in the fermioni…
Taking into account the PDFs, obtained by different Collaborations, the momentum transfer dependence of GPDs of the nucleons is obtained. The calculated electromagnetic and gravitomagnetic form factors of nucleons are used for the description of different form factors and the nucleons elastic scattering in a wide energy and momentum transfer region with a minimum number of fitting parameters. The electromagnetic and gravitomagnetic radii of the nucleon are calculated using the obtained momentum transfer dependence of GPDs with different forms of PDFs obtained by different Collaborations. The c…
Dispersion relations allow for a coherent description of the nucleon electromagnetic form factors measured over a large range of momentum transfer, $Q^2 \simeq 0 \ldots 35$ GeV$^2$. Including constraints from unitarity and perturbative QCD, we present a novel parametrisation of the absorptive parts of the various isoscalar and isovector nucleon form factors. Using the current world data, we obtain results for the electromagnetic form factors, nucleon radii and meson couplings. We stress the importance of measurements at large momentum transfer to test the predictions of perturbative QCD.
We present a theoretical parametrization of the nucleon electromagnetic form factors (FFs) based on a combination of chiral effective field theory and dispersion analysis. The isovector spectral functions on the two-pion cut are computed using elastic unitarity, chiral pion-nucleon amplitudes, and timelike pion FF data. Higher-mass isovector and isoscalar t-channel states are described by effective poles, whose strength is fixed by sum rules (charges, radii). Excellent agreement with the spacelike proton and neutron FF data is achieved up to Q^2 \sim 1 GeV^2. Our parametrization provides prope…
Quenched lattice QCD simulations and quenched chiral perturbation theory are used together for this study of strangeness in the nucleon. Dependences of the matrix elements on strange quark mass, valence quark mass and momentum transfer are discussed in both the lattice and chiral frameworks. The combined results of this study are in good agreement with existing experimental data and predictions are made for upcoming experiments. Possible future refinements of the theoretical method are suggested.
We study the electromagnetic properties of the nucleon and its excitations in a collective model. In the ensuing algebraic treatment all results for helicity amplitudes and form factors can be derived in closed form in the limit of a large model space. We discuss nucleon form factors and transverse electromagnetic couplings in photo- and electroproduction, including transition form factors that can be measured at new electron facilities.
Recent progress on the extraction of electromagnetic properties of nucleon resonance excitation through pion photo- and electroproduction is reviewed. Cross section data measured at MAMI, ELSA, and CEBAF are analyzed and compared to the analysis of other groups. On this basis, we derive longitudinal and transverse transition form factors for most of the four-star nucleon resonances. Furthermore, we discuss how the transition form factors can be used to obtain empirical transverse charge densities. Contour plots of the thus derived densities are shown for the Delta, Roper, S11, and D13 nucleon …
Taking into account PDFs obtained by various Collaborations, the momentum transfer dependence of GPDs of the pion are obtained. The calculated electromagnetic and gravitomagnetic form factors of the pions and nucleons are used for the description of the pion-nucleon elastic scattering in a wide energy and momentum transfer region with minimum fitting parameters.
We have evaluated nucleon and pion electromagnetic form factors using for the first time eigenfunctions of a light-front mass operator, reproducing a large set of energy levels, and constituent quark form factors in the one-body current. The comparison with the experimental data yields valuable information on the electromagnetic structure of light constituent quarks and on the different role played by their Dirac and Pauli form factors.
We analyze the electromagnetic form factors of the nucleon to fourth order in relativistic baryon chiral perturbation theory. We employ the recently proposed infrared regularization scheme and show that the convergence of the chiral expansion is improved as compared to the heavy fermion approach. We also discuss the inclusion of vector mesons and obtain an accurate description of all four nucleon form factors for momentum transfer squared up to Q^2 \simeq 0.4 GeV^2.
The electromagnetic form factors of the nucleon are calculated in an extended chiral constituent-quark model where the effective interaction is described by the exchange of pseudoscalar, vector, and scalar mesons. Two-body current-density operators, constructed consistently with the extended model Hamiltonian in order to preserve gauge invariance and current conservation, are found to give a significant contribution to the nucleon magnetic form factors and improve the estimates of the nucleon magnetic moments.
A relativistic quark model and a new set of wave functions of nucleon and Delta have been used to study the electromagnetic propertities of (1/2)^+ baryons and photoelectric production of Delta(1236).
We study the electromagnetic form factors of a nucleon in next-to-leading order chiral perturbation theory (CPT) in the case where one of the nucleons is off its mass shell. We calculate the leading nonanalytic contributions to relevant measures for the off-shell dependence in the limited kinematical range allowed.
We use the Nambu-Jona-Lasinio model as an effective quark theory to investigate the medium modifications of the nucleon electromagnetic form factors. By using the equation of state of nuclear matter derived in this model, we discuss the results based on the naive quark-scalar diquark picture, the effects of finite diquark size, and the meson cloud around the constituent quarks. We apply this description to the longitudinal response function for quasielastic electron scattering. RPA correlations, based on the nucleon-nucleon interaction derived in the same model, are also taken into account in …
We report on a recent calculation of all Roper-related electromagnetic transtions form factors, covering the range of energies that next-to-come planned experiments are expected to map. Direct reliable calculations were performed, within a Poincaré covariant approach of the three-body bound-state problem, up to $Q^2/m^2_N$=6; approximated then by applying the Schlessinger point method and the results eventually extended up to $Q^2/m^2_N\simeq$12 via analytic continuation.
Nucleon and pion electromagnetic form factors are evaluated in the spacelike region within a light-front constituent quark model, where eigenfunctions of a mass operator, reproducing a large set of hadron energy levels, are adopted and quark form factors are considered in the one-body current. The hadron form factors are sharply affected by the high momentum tail generated in the wave function by the one-gluon-exchange interaction. Useful information on the electromagnetic structure of light constituent quarks can be obtained from the comparison with nucleon and pion experimental data.
We study the electromagnetic form factors of the nucleon in a collective model of baryons. Using the algebraic approach to hadron structure, we derive closed expressions for both elastic and transition form factors, and consequently for the helicity amplitudes that can be measured in electro- and photoproduction. Effects of spin-flavor symmetry breaking and of swelling of hadrons with increasing excitation energy are considered.
A two component model describing the electromagnetic nucleon structure functions in the low-x region, based on generalized vector dominance and color dipole approaches is briefly described.
We have performed an evaluation of the individual up- and down-flavor contributions to the nucleon electromagnetic form factors within a relativistic constituent-quark model. It is found that the theoretical parameter-free predictions agree surprisingly well with recent experimental data from a flavor decomposition of the proton and neutron electromagnetic form factors for momentum transfers up to $Q^2\sim\;$3.5 GeV$^2$. It means that in this regime three-quark valence degrees of freedom dominate and other contributions, such as explicit mesonic effects, can at most play a minor role.
The effect of the self-energy on the photon-proton elastic scattering is investigated for the backward and the forward directions. The shape of the Thomson scattering at the photon energy $ω\to 0$ is broken by taking into account the self-energy of proton. The electromagnetic polarizabilities $\barα\pm\barβ$ are calculated by the lowest-order perturbative treatment.
We study the nucleon electromagnetic form factors in a quark-gluon core model framework, which can be viewed as an extension of the Isgur-Karl model of baryons. Using this picture we derive nucleon electromagnetic dipole form factors at low Q^2 and the deviation from the dipole form at high Q^2, that are consistent with the existing experimental data.
We present a simple covariant constituent diquark-quark model for the nucleon. The nucleon is assumed to be composed of a scalar diquark and a quark which interact via a quark exchange. Starting from the Bethe-Salpeter equation, the instantaneous approximation leads to a diquark-quark Salpeter equation. In the Mandelstam formalism, the electromagnetic form factors of the nucleon are calculated for momentum transfers up to $q^2 = - 3 \; (\mbox{GeV/c})^2$. A remarkable description of the experimental data is obtained. Especially, the model gives nearly the right values for the proton and (negati…
We present a relativistic interpretation for why the proton's ratio of electric to magnetic form factor falls and for why the ratio of the Pauli to Dirac form factor varies as 1/Q. Reproducing the observed electric form factor of the neutron then mandates the inclusion of the effects of the pion cloud.
Using hydrogen and deuterium targets, Compton scattering by the proton and neutron have been studied at the tagged photon beam of the MAMI (Mainz) accelerator using different experimental setups. The theoretical tools for the analysis of the experimental data have been investigated, as there are the nonsubtracted dispersion theory and the theory of quasi-free reactions on the proton and neutron bound in the deuteron. Experimental Compton scattering data are understood in the first and second resonance region with good precision. Precise electromagnetic polarizabilities and spin polarizabilitie…
The spatial distribution of charge and magnetization within the nucleon (proton and neutron) is encoded in the elastic electromagnetic form factors $G_E^{(p,n)}$ and $G_M^{(p,n)}$. These form factors have been precisely measured utilizing elastic electron scattering, and the combination of proton and neutron form factors allows for the separation of the up- and down-quark contributions to the nucleon form factors. We expand on our original analyses and extract the up- and down-quark contributions to the nucleon electromagnetic form factors from worldwide data with an emphasis on precise new da…
