Electric Form Factor Research Articles

Revealing dressed quarks via the proton's charge distribution.

The proton is arguably the most fundamental of nature's readily detectable building blocks. It is at the heart of every nucleus and has never been observed to decay. It is nevertheless a composite object, defined by its valence-quark content: u+u+d--i.e., two up (u) quarks and one down (d) quark; and the manner by which they influence, inter alia, the distribution of charge and magnetization within this bound state. Much of novelty has recently been learned about these distributions; and it now appears possible that the proton's momentum-space charge distribution possesses a zero. Experiments in the coming decade should answer critical questions posed by this and related advances; we explain how such new information may assist in charting the origin and impact of key emergent phenomena within the strong interaction. Specifically, we show that the possible existence and location of a zero in the proton's electric form factor are a measure of nonperturbative features of the quark-quark interaction in the standard model, with particular sensitivity to the running of the dressed-quark mass.

Electromagnetic transitions among octet and decuplet baryons in QCD

The magnetic dipole ${G}_{M}({Q}^{2})$, electric quadrupole ${G}_{E}({Q}^{2})$, and Coulomb quadrupole ${G}_{C}({Q}^{2})$ form factors, describing the spin-$3/2$ to spin-$1/2$ electromagnetic transitions, are investigated within the light cone QCD sum rules. The ${Q}^{2}$ dependence of these form factors, as well as ratios of electric quadrupole and Coulomb quadrupole form factors to the magnetic dipole form factors, are studied. We also compare our results on the magnetic dipole form factor with the prediction of the covariant spectator quark model.

Finite-volume corrections to charge radii

The finite-volume nature of lattice QCD entails a variety of effects that must be handled in the process of performing chiral extrapolations. Since the pion cloud that surrounds hadrons becomes distorted in a finite volume, hadronic observables must be corrected before one can compare with the experimental values. The electric charge radius of the nucleon is of particular interest when considering the implementation of finite-volume corrections. It is common practice in the literature to transform electric form factors from the lattice into charge radii prior to analysis. However, there is a fundamental difficulty with using these charge radii in a finite-volume extrapolation. The subtleties are a consequence of the absence of a continuous derivative on the lattice. A procedure is outlined for handling such finite-volume corrections, which must be applied directly to the electric form factors themselves rather than to the charge radii.

Study ofe+e−→pp¯via initial-state radiation atBABAR

The process e+e- --> p anti-p gamma is studied using 469 fb-1 of integrated luminosity collected with the BABAR detector at the PEP-II collider, at an e+e- center-of-mass energy of 10.6 GeV. From the analysis of the p anti-p invariant mass spectrum, the energy dependence of the cross section for e+e- --> p anti-p is measured from threshold to 4.5 GeV. The energy dependence of the ratio of electric and magnetic form factors, |G_E/G_M|, and the asymmetry in the proton angular distribution are measured for p anti-p masses below 3 GeV. We also measure the branching fractions for the decays J/psi --> p anti-p and psi(2S) --> p anti p.

Electromagnetic form factors of octet baryons in QCD

The electromagnetic form factors of octet baryons are estimated within light cone QCD sum rules method, using the most general form of the interpolating current for baryons. A comparison of our predictions on the magnetic dipole and electric form factors with the results of other approaches is performed.

Commutation Relations, Relativistic Invariance and Deriving the Value of the Fine-Structure Constant from Unitary Quantum Theory

The present article discusses the problems of relativistic invariance and commutation relations at unitary quantum theory. The scalar analogue of the main (principal) equation of the unitary quantum theory together with the Poisson equation are solved numerically in this paper. The value of the fine-structure constant, are found, which are in good agreement with the experiment. The evaluation of the electrical form factor of such a particle is also carried out.

Electron scattering in isotonic chains as a probe of the proton shell structure of unstable nuclei

Electron scattering on unstable nuclei is planned in future facilities of the GSI and RIKEN upgrades. Motivated by this fact, we study theoretical predictions for elastic electron scattering in the $N=82$, $N=50$, and $N=14$ isotonic chains from very proton-deficient to very proton-rich isotones. We compute the scattering observables by performing Dirac partial-wave calculations. The charge density of the nucleus is obtained with a covariant nuclear mean-field model that accounts for the low-energy electromagnetic structure of the nucleon. For the discussion of the dependence of scattering observables at low-momentum transfer on the gross properties of the charge density, we fit Helm model distributions to the self-consistent mean-field densities. We find that the changes shown by the electric charge form factor along each isotonic chain are strongly correlated with the underlying proton shell structure of the isotones. We conclude that elastic electron scattering experiments on isotones can provide valuable information about the filling order and occupation of the single-particle levels of protons.

Covariant spectator quark model description of theγ*Λ→Σ0transition

We study the $\gamma^\ast \Lambda \to \Sigma^0$ transition form factors by applying the covariant spectator quark model. Using the parametrization for the baryon core wave functions as well as for the pion cloud dressing obtained in a previous work, we calculate the dependence on the momentum transfer squared, $Q^2$, of the electromagnetic transition form factors. The magnetic form factor is dominated by the valence quark contributions. The final result for the transition magnetic moment, a combination of the quark core and pion cloud effects, turns out to give a value very close to the data. The pion cloud contribution, although small, pulls the final result towards the experimental value The final result, $\mu_{\Lambda\Sigma^0}= -1.486 \mu_N$, is about one and a half standard deviations from the central value in PDG, $\mu_{\Lambda\Sigma^0}= -1.61 \pm 0.08 \mu_N$. Thus, a modest improvement in the statistics of the experiment would permit the confirmation or rejection of the present result. It is also predicted that small but nonzero values for the electric form factor in the finite $Q^2$ region, as a consequence of the pion cloud dressing.

Nuclear size effects on hydrogenic atom energies: a semi-analytic formulation

The hydrogenic energy level shifts of a Dirac lepton due to the finite size of the nucleus are developed as a double power series in nuclear/atomic size ratio R and (squared) fine structure constant α2. The method relies on matching small and large radius solutions and is much simpler than the perturbation approach of Friar (1979 Ann. Phys. 122 151). Seven terms are obtained for nS1/2, six for nP1/2 and four for nP3/2. Analytic expressions are given for the standard uniform, Gaussian and exponential models; also numerical values for various toy proton models that approximate the proton electric form factor reasonably well.

Baryon electric dipole moments from strong CP violation

The electric dipole form factors and moments of the ground state baryons are calculated in chiral perturbation theory at next-to-leading order. We show that the baryon electric dipole form factors at this order depend only on two combinations of low-energy constants. We also derive various relations that are free of unknown low-energy constants. We use recent lattice QCD data to calculate all baryon EDMs. In particular, we find d_n = -2.9\pm 0.9 and d_p = 1.1\pm 1.1 in units of 10^{-16} e \theta_0 cm. Finite volume corrections to the moments are also worked out. We show that for a precision extraction from lattice QCD data, the next-to-leading order terms have to be accounted for.

Δ-resonance contribution to the two-photon exchange amplitude

We consider two-photon exchange (TPE) in the elastic electron-proton scattering and study the contribution arising from the production of Delta(1232) resonance in the intermediate state. We calculate all three TPE amplitudes (generalized form factors), and find that the Delta contribution mainly influences generalized electric form factor (contrary to the elastic contribution, which affects magnetic form factor), and the effect grows with Q^2. If the corresponding correction is applied to the recent polarization transfer measurements of proton form factors, their results will change markedly. Thus we suggest that TPE corrections due to inelastic intermediate states are important to polarization experiments at high Q^2, and should not be neglected.

Octet baryon electromagnetic form factors in nuclear medium

We study the octet baryon electromagnetic form factors in nuclear matter using the covariant spectator quark model extended to the nuclear matter regime. The parameters of the model in vacuum are fixed by the study of the octet baryon electromagnetic form factors. In nuclear matter the changes in hadron properties are calculated by including the relevant hadron masses and the modification of the pion–baryon coupling constants calculated in the quark–meson coupling model. In nuclear matter the magnetic form factors of the octet baryons are enhanced in the low Q2 region, while the electric form factors show a more rapid variation with Q2. The results are compared with the modification of the bound proton electromagnetic form factors observed at Jefferson Lab. In addition, the corresponding changes for the bound neutron are predicted.

Precise form factors from elastic electron scattering

Experiments to determine the electric and magnetic form factors of nucleons have been performed for over half a century. This article gives an overview of the current state of our knowledge and discusses new features discovered in recent high precision experiments.

Parity-Violating Electron Scattering and the Electric and Magnetic Strange Form Factors of the Nucleon

Measurements of the neutral weak-vector form factors of the nucleon provide unique access to the strange quark content of the nucleon. These form factors can be studied by using parity-violating electron scattering. A comprehensive program of experiments has been performed at three accelerator laboratories to determine the role of strange quarks in the electromagnetic form factors of the nucleon. This article reviews the remarkable technical progress associated with this program, describes the various methods used in the different experiments, and summarizes the physics results along with recent theoretical calculations.

Electromagnetic multipole moments of elementary spin-1/2, 1, and3/2particles

We study multipole decompositions of the electromagnetic currents of spin-$1/2$, 1, and $3/2$ particles described in terms of representation-specific wave equations which are second order in the momenta and which emerge within the recently elaborated Poincar\'e covariant-projector method, where the respective Lagrangians explicitly depend on the Lorentz group generators of the representations of interest. The currents are then the ordinary linear Noether currents related to phase invariance, and present themselves always as two-terms motion--plus spin-magnetization currents. The spin-magnetization currents appear weighted by the gyromagnetic ratio $g$, a free parameter in the method which we fix either by unitarity of forward Compton scattering amplitudes in the ultraviolet for spin-1 and spin-$3/2$, or in the spin-$1/2$ case, by their asymptotic vanishing, thus ending up in all three cases with the universal $g$ value of $g=2$. Within the method under discussion, we calculate the electric multipoles of the above spins for the spinor, the four-vector, and the four-vector--spinor representations, and find it favorable in some aspects, specifically in comparison with the conventional Proca and Rarita-Schwinger frameworks. We furthermore attend to the most general non-Lagrangian spin-$3/2$ currents, which are allowed by Lorentz invariance to be up to third order in the momenta and construct the linear-current equivalent of identical multipole moments of one of them. We conclude that nonlinear non-Lagrangian spin-$3/2$ currents are not necessarily more general and more advantageous than the linear spin-$3/2$ Lagrangian current emerging within the covariant-projector formalism. Finally, we test the representation dependence of the multipoles by placing spin-1 and spin-$3/2$ in the respective $(1,0)\ensuremath{\bigoplus}(0,1)$ and $(3/2,0)\ensuremath{\bigoplus}(0,3/2)$ single-spin representations. We observe representation independence of the charge monopoles and the magnetic dipoles, in contrast to the higher multipoles, which turn out to be representation-dependent. In particular, we find the bi-vector $(1,0)\ensuremath{\bigoplus}(0,1)$ to be characterized by an electric quadrupole moment of opposite sign to the one found in $(1/2,1/2)$, and consequently to the $W$ boson. This observation allows us to explain the positive electric quadrupole moment of the $\ensuremath{\rho}$ meson extracted from recent analyses of the $\ensuremath{\rho}$ meson electric form factor. Our finding points toward the possibility that the $\ensuremath{\rho}$-meson could transform as part of an antisymmetric tensor with an ${a}_{1}$ mesonlike state as its representation companion, a possibility consistent with the empirically established $\ensuremath{\rho}$ and ${a}_{1}$ vector meson dominance of the hadronic vector and axial-vector currents.

Timelike and spacelike electromagnetic form factors of nucleons, a unified description

The extended Lomon-Gari-Kr\"umpelmann model of nucleon electromagnetic form factors, which embodies $\ensuremath{\rho}$, ${\ensuremath{\rho}}^{\ensuremath{'}}$, $\ensuremath{\omega}$, ${\ensuremath{\omega}}^{\ensuremath{'}}$, and $\ensuremath{\phi}$ vector meson contributions and the perturbative QCD high momentum transfer behavior has been extended to the timelike region. Breit-Wigner formulas with momentum-dependent widths have been considered for broad resonances in order to have a parametrization for the electromagnetic form factors that fulfills, in the timelike region, constraints from causality, analyticity, and unitarity. This analytic extension of the Lomon-Gari-Kr\"umpelmann model has been used to perform a unified fit to all the nucleon electromagnetic form factor data, in the spacelike and timelike region (where form factor values are extracted from ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\leftrightarrow}N\overline{N}$ cross sections data). The knowledge of the complete analytic structure of form factors enables predictions at extended momentum transfer, and also of timelike observables such as the ratio between electric and magnetic form factors and their relative phase.

Exploring strange nucleon form factors on the lattice

We discuss techniques for evaluating sea quark contributions to hadronic form factors on the lattice and apply these to an exploratory calculation of the strange electromagnetic, axial, and scalar form factors of the nucleon. We employ the Wilson gauge and fermion actions on an anisotropic ${24}^{3}\ifmmode\times\else\texttimes\fi{}64$ lattice, probing a range of momentum transfer with ${Q}^{2}<1\text{ }\text{ }{\mathrm{GeV}}^{2}$. The strange electric and magnetic form factors, ${G}_{E}^{s}({Q}^{2})$ and ${G}_{M}^{s}({Q}^{2})$, are found to be small and consistent with zero within the statistics of our calculation. The lattice data favor a small negative value for the strange axial form factor ${G}_{A}^{s}({Q}^{2})$ and exhibit a strong signal for the bare strange scalar matrix element $⟨N|\overline{s}s|N{⟩}_{0}$. We discuss the unique systematic uncertainties affecting the latter quantity relative to the continuum, as well as prospects for improving future determinations with Wilson-like fermions.

New Precision Limit on the Strange Vector Form Factors of the Proton

The parity-violating cross-section asymmetry in the elastic scattering of polarized electrons from unpolarized protons has been measured at a four-momentum transfer squared Q2 = 0.624 GeV2 and beam energy E(b) = 3.48 GeV to be A(PV) = -23.80 ± 0.78(stat) ± 0.36(syst) parts per million. This result is consistent with zero contribution of strange quarks to the combination of electric and magnetic form factors G(E)(s) + 0.517G(M)(s) = 0.003 ± 0.010(stat) ± 0.004(syst) ± 0.009(ff), where the third error is due to the limits of precision on the electromagnetic form factors and radiative corrections. With this measurement, the world data on strange contributions to nucleon form factors are seen to be consistent with zero and not more than a few percent of the proton form factors.

Nucleon andΔ(1232)form factors at low momentum transfer and small pion masses

An expansion of the electromagnetic form factors of the nucleon and $\ensuremath{\Delta}(1232)$ in small momentum transfer and pion mass is performed in a manifestly covariant EFT framework consistent with chiral symmetry and analyticity. We present the expressions for the nucleon and $\ensuremath{\Delta}(1232)$ electromagnetic form factors, charge radii, and electromagnetic moments in the framework of $SU(2)$ baryon chiral perturbation theory, with nucleon and $\ensuremath{\Delta}$-isobar degrees of freedom, to next-to-leading order. Motivated by the results for the proton electric radius obtained from the muonic-hydrogen atom and electron-scattering process, we extract values for the second derivative of the electric form factor which is a genuine prediction of the ${p}^{3}$ $\mathrm{B}\ensuremath{\chi}\mathrm{PT}$. The chiral behavior of radii and moments is studied and compared to that obtained in the heavy-baryon framework and lattice QCD. The chiral behavior of $\ensuremath{\Delta}(1232)$-isobar properties exhibits cusps and singularities at the threshold of $\ensuremath{\Delta}\ensuremath{\rightarrow}\ensuremath{\pi}N$ decay, and their physical significance is discussed.

Calibration of drift chambers and calorimeter of BigBite spectrometer

Method of calibration of the calorimeter and drift chambers of the BigBite spectrometer having been used in the experiment on measuring the neutron electric form-factor is presented. The BigBite spectrometer provided measurement of the direction and momentum of scattered electron by means of measuring its trajectory after passing through the magnetic field. Calibration of the set of detectors of the BigBite spectrometer was important for success of the experiment.