Charge Form Factor Research Articles

Instanton contribution to the pion electromagnetic form factor atQ2>1GeV2

We study the effects of instantons on the charged pion electromagnetic form factor at intermediate momenta. In the single instanton approximation (SIA), we predict the pion form factor in the kinematic region ${Q}^{2}=2--10{\mathrm{GeV}}^{2}.$ By developing the calculation in a mixed time-momentum representation, it is possible to maximally reduce the model dependence and to calculate the form factor directly. We find the intriguing result that the SIA calculation coincides with the vector dominance monopole form, up to a surprisingly high momentum transfer ${Q}^{2}\ensuremath{\sim}10{\mathrm{GeV}}^{2}.$ This suggests that vector dominance for the pion holds beyond low energy nuclear physics.

The neutron charge form factor and target analyzing powers from [formula omitted] scattering

The charge form factor of the neutron has been determined from asymmetries measured in quasi-elastic 3He(e→,e′n) at a momentum transfer of 0.67 (GeV/c)2. In addition, the target analyzing power, Ayo, has been measured to study effects of final state interactions and meson exchange currents.

Measurement of the tensor analyzing powers T20 and T21 in elastic electron-deuteron scattering.

The tensor analyzing power components T20 and T21 have been measured in elastic electron-deuteron scattering at the 2 GeV electron storage ring VEPP-3, Novosibirsk, in a four-momentum transfer range from 8.4 to 21.6 fm(-2). A new polarized internal gas target with an intense cryogenic atomic beam source was used. The new data determine the deuteron form factors G(C) and G(Q) in an important range of momentum transfer where the first node of the deuteron monopole charge form factor is located. The new results are compared with previous data and with some theoretical predictions.

Extraction of the neutron charge form factor Gn E(Q2) from the charge form factor of deuteron Gd C(Q2)

We extract the neutron charge form factor from the charge form factor of deuteron obtained from $T_{20}(Q^2)$ data at $0\le Q^2\le$ 1.717 (GeV$^2$). The extraction is based on the relativistic impulse approximation in the instant form of the relativistic Hamiltonian dynamics. Our results (12 new points) are compatible with existing values of the neutron charge form factor of other authors. We propose a fit for the whole set (35 points) taking into account the data for the slope of the form factor at $Q^2 = 0$.

Nucleon charge and magnetization densities from Sachs form factors

Relativistic prescriptions relating Sachs form factors to nucleon charge and magnetization densities are used to fit recent data for both the proton and the neutron. The analysis uses expansions in complete radial bases to minimize model dependence and to estimate the uncertainties in radial densities due to limitation of the range of momentum transfer. We find that the charge distribution for the proton is significantly broad than its magnetization density and that the magnetization density is slightly broader for the neutron than the proton. The neutron charge form factor is consistent with the Galster parametrization over the available range of Q^2, but relativistic inversion produces a softer radial density. Discrete ambiguities in the inversion method are analyzed in detail. The method of Mitra and Kumari ensures compatibility with pQCD and is most useful for extrapolating form factors to large Q^2.

From soft to hard regime in elastic pion-pion scattering above resonances

We discuss the onset of the dominance of the Glauber-Gribov-Landshoff (GGL) component of pQCD hard two-gluon (2G) exchange contribution to hard elastic $\pi\pi$ scattering at moderate energies . Such a hard $\pi\pi$ scattering could via final state interaction on the $\gamma \gamma \to \pi^+ \pi^-$ reaction in which pQCD quark-exchange contribution is known to be short of strength. While in the nonrelativistic approximation the GGL amplitude is known to be free of suppression by the pion form factor, we show that in the relativistic light-cone approach it acquires a residual, albeit a weak, suppression. Furthermore,z the same mechanism it is free of the end-point contributions. We evaluation the GGL amplitude with a model light-cone wave function consistent with the pion charge form factor data. The soft contribution to elastic $\pi\pi$ scattering is estimated based on the $NN$ and $\pi N$ total cross section data and Regge factorization, which gives the $\pi\pi$ total cross sections consistent with the ones deduced earlier from the absorption model analysis of the $\pi N \to X N, X \Delta$ data. We evaluate the large-$|t|$ tail of the soft amplitude within the Regge absorption models. We find that while in the same sign $\pi^\pm\pi^\pm$ scattering the hard GGL mechanism takes over at $|t|\gsim$ 3 GeV$^{-2}$, in the opposite-sign $\pi^\pm\pi^\mp$ scattering the hard GGL mechanism $|t|\lsim$ 4 GeV$^{-2}$.

Effects of an electromagnetic quark form factor on meson properties

A form factor is introduced in the quark electromagnetic current. Its effect is analyzed on charge mean square radii and form factors in the mesonic sector. The decay of a vector meson into lepton–antilepton pair is also affected. Two different expressions for the form factors, and two different types of quark potential are tested and some relativistic kinematical corrections are proposed. In any case the introduction of a quark form factor greatly improves the agreement with experimental data.

Nucleon momentum distribution in deuteron and other nuclei within the light-front dynamics method

The relativistic light-front dynamics (LFD) method has been shown to give a correct description of the most recent data for the deuteron monopole and quadrupole charge form factors obtained at the Jefferson Laboratory for elastic electron-deuteron scattering for six values of the squared momentum transfer between 0.66 and 1.7 (GeV/c)$^{2}$. The good agreement with the data is in contrast with the results of the existing non-relativistic approaches. In this work we firstly make a complementary test of the LFD applying it to calculate another important characteristic, the nucleon momentum distribution $n(q)$ of the deuteron using six invariant functions $f_{i}$ $(i=1,...,6)$ instead of two ($S$- and $D$-waves) in the nonrelativistic case. The comparison with the $y$-scaling data shows the decisive role of the function $f_{5}$ which at $q\geq$ 500 MeV/c exceeds all other $f$-functions (as well as the $S$- and $D$-waves) for the correct description of $n(q)$ of the deuteron in the high-momentum region. Comparison with other calculations using $S$- and $D$-waves corresponding to various nucleon-nucleon potentials is made. Secondly, using clear indications that the high-momentum components of $n(q)$ in heavier nuclei are related to those in the deuteron, we develop an approach within the natural orbital representation to calculate $n(q)$ in $(A,Z)$-nuclei on the basis of the deuteron momentum distribution. As examples, $n(q)$ in $^{4}$He, $^{12}$C and $^{56}$Fe are calculated and good agreement with the $y$-scaling data is obtained.

Electromagnetic structure of the nucleon in the perturbative chiral quark model

We apply the perturbative chiral quark model (PCQM) at one loop to analyze the electromagnetic structure of nucleons. This model is based on an effective Lagrangian, where baryons are described by relativistic valence quarks and a perturbative cloud of Goldstone bosons. Including the electromagnetic interaction we first develop the formalism up to one loop in the Goldstone boson fluctuation relying on renormalization by use of counterterms. Local gauge invariance is satisfied both on the Lagrangian level and also for the relevant baryon matrix elements in the Breit frame. We apply the formalism to obtain analytical expressions for the nucleon charge and magnetic form factors, which are expressed in terms of fundamental parameters of low-energy pion-nucleon physics (weak pion decay constant, axial nucleon coupling, strong pion-nucleon form factor) and of only one model parameter (radius of the nucleonic three-quark core). A detailed numerical analysis of the nucleon magnetic moments, charge and magnetic radii, and also the momentum dependence of form factors is presented.

Rearranging pionless effective field theory

We point out a redundancy in the operator structure of the pionless effective field theory, EFT(π̵), which dramatically simplifies computations. This redundancy is best exploited by using dibaryon fields as fundamental degrees of freedom. In turn, this suggests a new power counting scheme which sums range corrections to all orders. We explore this method with a few simple observables: the deuteron charge form factor, np→d γ, and Compton scattering from the deuteron. Unlike EFT(π̵), the higher-dimension operators involving electroweak gauge fields are not renormalized by the s-wave strong interactions, and therefore do not scale with inverse powers of the renormalization scale. Thus, naive dimensional analysis of these operators is sufficient to estimate their contribution to a given process.

Neutron charge form factor at largeq2

The neutron charge form factor ${G}_{\mathrm{En}}(q)$ is determined from an analysis of the deuteron quadrupole form factor ${F}_{C2}(q)$ data. Recent calculations, based on a variety of different model interactions and currents, indicate that the contributions associated with the uncertain two-body operators of shorter range are relatively small for ${F}_{C2}(q),$ even at large momentum transfer q. Hence, ${G}_{\mathrm{En}}(q)$ can be extracted from ${F}_{C2}(q)$ at large ${q}^{2}$ without undue systematic uncertainties from theory.

Relativistic quark spin coupling effects in the correlations between nucleon electroweak properties

We investigate the effect of different relativistic spin couplings of constituent quarks on nucleon electroweak properties. Within each quark spin coupling scheme the correlations between static electroweak observables are found to be independent of the particular shape of the momentum part of the nucleon light-front wave function. The neutron charge form factor is very sensitive to different choices of spin coupling schemes once the magnetic moment is fitted to the experimental value. However, it is found rather insensitive to the details of the momentum part of the three-quark wave function model.

Ground state of the 4α + Λ nucleus within the 4α+Λ cluster model

The s-wave bound state of the 4α+Λ system is investigated. The relevant solution to the Schrodinger equation is expanded in the basis formed by the eigenfunctions of Hamiltonian for the 4α subsystem. Differential equations for Yakubovsky components are employed to calculate basis functions. Phenomenological potentials for αα and αΛ interactions are used. In the 4α system, additional three-particle potentials for the interaction between α clusters are introduced in such a way as to reproduce the experimental data on the binding energies, the root-mean-square radii, and the charge form factors for the 12C and the 16O nucleus. The binding energy, the root-mean-square radius, and the hyperon distribution in the ground state of the Λ 17 O nucleus are calculated. The results of the calculations are in good agreement with those obtained on the basis of the 16O+Λ two-particle model with the phenomenological Woods-Saxon potential.

Evaluation of cluster expansions and correlated one-body properties of nuclei

Three different cluster expansions for the evaluation of correlated one-body properties of s-p and s-d shell nuclei are compared. Harmonic oscillator wave functions and Jastrow type correlations are used, while analytical expressions are obtained for the charge form factor, density distribution, and momentum distribution by truncating the expansions and using a standard Jastrow correlation function f. The harmonic oscillator parameter b and the correlation parameter \beta have been determined by a least-squares fit to the experimental charge form factors in each case. The information entropy of nuclei in position-space (S_r) and momentum-space (S_k) according to the three methods are also calculated. It is found that the larger the entropy sum S=S_r+S_k (the information content of the system) the smaller the values of \chi^2. This indicates that S is a criterion of the quality of a given nuclear model, according to the maximum entropy principle. Only two exceptions to this rule, out of many cases examined, were found. Finally an analytic expression for the so-called "healing" or "wound" integrals is derived with the function f considered, for any state of the relative two-nucleon motion and their values in certain cases are computed and compared.

On a possible estimation of the constituent-quark parameters from Jefferson Lab experiments on the pion form factor

The charge form factor of the pion is calculated for the momentum transfer range of the Jefferson Lab experiments. The approach is based on the instant form of the relativistic Hamiltonian dynamics. It is shown that the form-factor dependence on the choice of the model for the quark wave function in the pion is weak, while the dependence on the constituent-quark mass is rather significant. It is possible to estimate the mass of the constituent quark and the sum of the anomalous magnetic moments of the u- and $\bar d$ -quarks from the JLab experiments.

Moments of the neutron charge form factor and the N --> Delta quadrupole transition.

Recent data allow a new parametrization of the neutron charge form factor GnE. A parameter-free quark-model relation between GnE and the N-->Delta quadrupole form factor G(N-->Delta)C2 is used to predict G(N-->Delta)C2 from GnE data. In particular, <r2n> is related to N-->Delta quadrupole moment Q(N-->Delta), while <r4n> connects to the N-->Delta quadrupole transition radius <r2(N-->Delta)>. From the latter we derive an experimental value for the charge radius of the light constituent quarks r(gamma(q)) = 0.8 fm. Finally, the C2/M1 ratio in pion electroproduction is predicted from the elastic neutron form factor data.

Measurement of the charged pion electromagnetic form factor.

Separated longitudinal and transverse structure functions for the reaction 1H(e,e(')pi(+))n were measured in the momentum transfer region Q2 = 0.6--1.6 (GeV/c)(2) at a value of the invariant mass W = 1.95 GeV. New values for the pion charge form factor were extracted from the longitudinal cross section by using a recently developed Regge model. The results indicate that the pion form factor in this region is larger than previously assumed and is consistent with a monopole parametrization fitted to very low Q2 elastic data.

Elastic electron scattering from light nuclei

The charge and magnetic form factors of light nuclei, mainly for mass number A≤4, provide a sensitive test of our understanding of nuclei. A number of “exact” calculations of the wave functions starting from the nucleon-nucleon interaction are available. The treatment of two-body effects needed in the calculation of the electromagnetic form factors has made significant progress. Many electron scattering experiments have provided an extensive data base from which the various (mainly elastic) form factors can be extracted. This review discusses the data and the determination of the form factors, and compares them to the results of theory.

VIOLATIONS OF LORENTZ COVARIANCE IN LIGHT FRONT QUARK MODELS

Electromagnetic form factors of the nucleon from relativistic quark models are analyzed: Results from null-plane projection of the Feynman triangle diagram are compared with a Bakamjian–Thomas model. The magnetic form factors of the models differ by about 15% at spacelike momentum transfer 0.5 GeV2, while the charge form factors are much closer. Spurious contributions to electromagnetic form factors due to violations of rotational symmetry are eliminated for both models. One method changes magnetic form factors by about 10%, whereas the charge form factors remain nearly the same. Another one changes the charge form factor of the Bakamjian–Thomas model by more than 50%.

Radiation from an electron bunch flying over a surface wave

Radiation generated by the passage of a monoenergetic electron bunch above the surface wave excited in plane interface between homogeneous media with different dielectric constants is investigated. For the surface wave of general profile the radiation intensity is expressed via the radiated power from a single charge and bunch form factor. Various types of transverse and longitudinal distributions of electrons in the bunch have been considered including Gaussian, asymmetrical Gaussian, two Gaussian and rectangular distribution with asymmetrical exponential tails. Conditions are specified under which the coherent radiation essentially exceeds the incoherent part.