Electric Form Factor Research Articles

Calculations of the deuteron form factors

On the received coefficients of the analytical forms for deuteron wave function in coordinate representation in form r^(l+1)*exp(-A*r) for the modern realistic nucleon-nucleon potentials NijmI, NijmII, Nijm93, Reid93 and Argonne v18 are calculated charge GC(p), quadrupole GQ(p) and magnetic GM(p) deuteron form factors. An original dipole fit for proton and neutron isoscalar electric and magnetic form factors is used for calculations. Theoretical calculations of values of the deuteron form factor are compared with their experimental data of world collaborations (Bates, BLAST, Bonn, JLab, Mainz, Naval Research Lab, NIKHEF, Orsay, Saclay, SLAC, Stanford, VEPP3 and VEPP4) and reviews (Abbott, Boden, Garcon and Karpius). The change of the sign of form factors is in the pulse regions at 4.7-4.9 fm-1 for GC; at 12.8-14.7 fm-1 for GQ; at 6.3-8.1 and 11.4-12.2 fm-1 for GM. The theoretical values for the form factors GQ(0) and GM(0) were calculated at the boundary condition for the momentum at p2=0. Calculated positions of the zero for deuteron form factors are compared with values for other potential models. The peculiarities of parametrizations of deuteron form factors for theoretical approaches and fits of theoretical calculations to experimental values, which are described in the cited literature, are analyzed. Formulas for spherical and quadrupole form factors are writed, which are expressed in terms of the coefficients for the indicated deuteron wave function. At large values of momentum the asymptotics of the deuteron form factors are determined by the coefficients of the analytical forms for deuteron wave function, nucleon isoscalar form factors and the order of momentum in the denominator. The further use of deuteron form factors for obtaining polarization observables in processes involving deuteron as a projectile is discussed.

Spin polarization of Λ hyperons in at BESIII

The BESIII collaboration here reports the first observation of polarized Λ and hyperons produced in two different processes: i) the resonant , using a data sample of 1.31 × 109J/ψ events and ii) the non-resonant , using a 66.9 pb−1 data sample collected at . In , the phase between the electric and the magnetic amplitude is measured for the first time to be 42.3° ± 0.6° ± 0.5°. The multi-dimensional analysis enables a model-independent measurement of the decay parameters for and . The obtained value α− = 0.750 ± 0.009 ± 0.004 differs with 5σ from the PDG value. This value, together with the measurement α+ = −0.758 ± 0.010 ± 0.007 allow for the most precise test of CP violation in decays so far: ACP = ( α− + α+)/(α− − α+) of −0.006 ± 0.012 ± 0.007. The decay asymmetry is measured for the first time. The reaction at enables a first complete measurement of the time-like electric and magnetic form factor of any baryon, of the modulus of the ratio R = |GE/GM| and of the relative phase ΔΦ = ΦE − ΦM. With the decay asymmetry parameters from the J/ψ data, the obtained values are R = 0.96 ± 0.14 ± 0.02 and ΔΦ = 37° ± 12° ± 6°. In addition, the cross section has been measured with unprecedented precision to be σ = 119.0 ± 5.3 ± 5.1 pb, which corresponds to an effective form factor of |G| = 0.123 ± 0.003 ± 0.003.

α(Zα)5m finite-nuclear-size contribution to the energy levels in light muonic atoms

We present a theoretical consideration of the radiative two-photon finite-nuclear-size contributions to the Lamb shift in a light muonic atom. They are of the order of $\ensuremath{\alpha}{(Z\ensuremath{\alpha})}^{5}m$ and may depend differently on $m{R}_{N}$. The contributions are due to the electronic and muonic vacuum polarization and the muon self-energy. The consideration is done within the external field approximation. We also found the leading logarithmic finite-nuclear-size contributions in the next order. One of them is of the order $\ensuremath{\alpha}{(Z\ensuremath{\alpha})}^{6}{ln}^{2}(Z\ensuremath{\alpha})\phantom{\rule{0.16em}{0ex}}{(m{R}_{N})}^{2}m$ and the other is of the order ${\ensuremath{\alpha}}^{2}{(Z\ensuremath{\alpha})}^{5}{ln}^{2}({m}_{e}{R}_{N})\phantom{\rule{0.16em}{0ex}}{(m{R}_{N})}^{3}m$. Special attention is paid to higher-order effects in muonic hydrogen and the related applications of various parametrizations of the proton electric form factors. We also consider the general expressions in coordinate space for the finite-size radiative contributions to the Lamb shift in two-body muonic atoms. The numerical results are present for the atoms with $Z\ensuremath{\le}10$.

HCAL-J: hadron calorimeter for the study of nucleon form factors at Jefferson Lab

ABSTRACTHCAL-J is a hadron calorimeter under construction at JLAB in Newport News, VA (USA).The main interest of the JLAB physics is the study of the hadron matter properties, using a longitudinally polarised electron beam; in particular, researchers investigate the electromagnetic form factors of nuclei and nucleons using the Continuous Electron Beam Accelerator Facility (CEBAF) accelerator, which provides a beam of 12 GeV electrons. The upgrade to higher energies allows measurements at high values of Q2 and a more in-depth study of the internal structure of the hadron matter.To this purpose, Hall A collaboration is building the SuperBigBite Spectrometer (SBS), which consists of a series of elements including a dipole magnet to curve the trajectory of the recoil particles, and a series of Gas Electron Multiplier (GEM) to track the particles. Moreover, two analyzers for the measurement of the polarisation components and a hadron calorimeter, HCAL-J, to measure the particle energy, are used in order to apply the so-called recoil polarisation method, which consists in measuring both the longitudinal and transverse polarisation of the scattered nucleon.The study, through SBS, of the electromagnetic form factors of nucleons allows obtaining the ratio between these two components, which results to be proportional to the ratio between the electric and magnetic form factors of the nucleon.HCAL-J is a sampling calorimeter useful to measure the energy of the recoil nucleon; its active area consists of 288 modules that include a matrix with 24 modules in height and 12 in width. There are optical fibres in between each module, connected to a photomultiplier, in order to look at the light from the scintillating material and convert it into an electric signal, related to the energy of the incident particle.

The electromagnetic form factors of Λ hyperon in e+e−→Λ̄Λ

We study the electromagnetic form factors of [Formula: see text] hyperon in the time-like region using the experimental data in the exclusive production of [Formula: see text] pair in electron–positron annihilation. We present a pQCD inspired parametrization of [Formula: see text] and [Formula: see text] with only two parameters, and we consider a suppression mechanism of the electric form factor [Formula: see text] compared to the magnetic form factor [Formula: see text]. The parameters are determined through fitting our parametrization to the data of the effective form factor [Formula: see text] from the DM2, BaBar and BESIII Collaborations in the reaction [Formula: see text]. We use the parametrizations for [Formula: see text] and [Formula: see text] to calculate the Born cross-sections as well as the ratio [Formula: see text]. Except the threshold region, our parametrization can describe the known behavior of the existing data of effective form factor, Born cross-section and the ratio [Formula: see text] from the BaBar, DM2 and BESIII Collaborations. We also predict the double spin polarization observables [Formula: see text], [Formula: see text] and [Formula: see text] in [Formula: see text] which could provide more information on the size of the lambda EMFFs as well as their phase angles.

Electromagnetic form factors of singly heavy baryons in the self-consistent SU(3) chiral quark-soliton model

The self-consistent chiral quark-soliton model is a relativistic pion mean-field approach in the large $N_c$ limit, which describes both light and heavy baryons on an equal footing. In the limit of the infinitely heavy mass of the heavy quark, a heavy baryon can be regarded as $N_c-1$ valence quarks bound by the pion mean fields, leaving the heavy quark as a color static source. The structure of the heavy baryon in this scheme is mainly governed by the light-quark degrees of freedom. Based on this framework, we evaluate the electromagnetic form factors of the lowest-lying heavy baryons. The rotational $1/N_c$ and strange current quark mass corrections in linear order are considered. We discuss the electric charge and magnetic densities of heavy baryons in comparison with those of the nucleons. The results of the electric charge radii of the positive-charged heavy baryons show explicitly that the heavy baryon is a compact object. The electric form factors are presented. The form factor of $\Sigma_c^{++}$ is compared with that from a lattice QCD. We also discuss the results of the magnetic form factors. The magnetic moments of the baryon sextet with spin 1/2 and the magnetic radii are compared with other works and the lattice data.

$$N^*$$ N ∗ form Factors Based on a Covariant Quark Model

We discuss the results of the covariant spectator quark model for the several $\gamma^\ast N \to N^\ast$ transitions, where $N$ is the nucleon and $N^\ast$ a nucleon excitation. More specifically, we present predictions for the form factors and transition amplitudes associated with the resonances $N(1440)1/2^+$, $N(1535)1/2^-$, $N(1520)3/2^-$, $\Delta(1620)1/2^-$ and $N(1650)1/2^-$. The estimates based on valence quark degrees of freedom are compared with the available data, particularly with the recent Jefferson Lab data at low and large momentum transfer ($Q^2$). In general, the estimates are in good agreement with the empirical data for $Q^2 >2$ GeV$^2$, with a few exceptions. The results are discussed in terms of the role of the valence quarks and the meson cloud excitations for the different resonances $N^\ast$. We also review our results for the resonance $\Delta(1232)3/2^+$ and discuss the relevance of the pion cloud component for the magnetic dipole form factor and the electric and Coulomb quadrupole form factors.

Polarization observables and T-noninvariance in the weak charged current induced electron proton scattering

In this work, we have studied the total scattering cross section ($\sigma$), differential scattering cross section ($d\sigma/dQ^2$) as well as the longitudinal ($P_L(E_e,Q^2)$), perpendicular ($P_P(E_e,Q^2)$), and transverse ($P_T(E_e,Q^2)$) components of the polarization of the final hadron ($n$, $ \Lambda$ and $\Sigma^0$) produced in the electron proton scattering induced by the weak charged current. We have not assumed T-invariance which allows the transverse component of the hadron polarization perpendicular to the production plane to be non-zero. The numerical results are presented for all the above observables and their dependence on the axial vector form factor and the weak electric form factor are discussed. The present study enables the determination of the axial vector nucleon-hyperon transition form factors at high $ Q^2$ in the strangeness sector which can provide test of the symmetries of the weak hadronic currents like T-invariance and SU(3) symmetry while assuming the hypothesis of conserved vector current and partial conservation of axial vector current.

Strange nucleon electromagnetic form factors from lattice QCD

We evaluate the strange nucleon electromagnetic form factors using an ensemble of gauge configurations generated with two degenerate maximally twisted mass clover-improved fermions with mass tuned to approximately reproduce the physical pion mass. In addition, we present results for the disconnected light quark contributions to the nucleon electromagnetic form factors. Improved stochastic methods are employed leading to high-precision results. The momentum dependence of the disconnected contributions is fitted using the model-independent z-expansion. We extract the magnetic moment and the electric and magnetic radii of the proton and neutron by including both connected and disconnected contributions. We find that the disconnected light quark contributions to both electric and magnetic form factors are nonzero and at the few percent level as compared to the connected. The strange form factors are also at the percent level but more noisy yielding statistical errors that are typically within one standard deviation from a zero value.

New low-Q2 measurements of the $\gamma^{\ast}N\rightarrow\Delta (1232)$ γ * N → Δ ( 1232 ) Coulomb quadrupole form factor, pion cloud parametrizations and Siegert’s theorem

The novel measurements of the $\gamma^\ast N \to \Delta(1232)$ Coulomb quadrupole form factor in the range $Q^2=0.04$--0.13 GeV$^2$ changed the trend of the previous data. With the new data the electric and Coulomb form factors are both in remarkable agreement with estimates of the pion cloud contributions to the quadrupole form factors at low $Q^2$. The pion cloud contributions to the electric and Coulomb form factors can be parametrized by the relations $G_E \propto G_{En}/ \left(1 + \frac{Q^2}{2M_\Delta(M_\Delta-M)}\right)$ and $G_C \propto G_{En}$, where $G_{En}$ is the neutron electric form factor, and $M$, $M_\Delta$ are the nucleon and $\Delta$ masses, respectively. Those parametrizations are in full agreement with Siegert's theorem, which states that $G_E= \frac{M_\Delta-M}{2M_\Delta} G_C$ at the pseudothreshold, when $Q^2=-(M_\Delta -M)^2$, and improve previous parametrizations. Also a small valence quark component estimated by a covariant quark model contributes to this agreement. The combination of the new data with the new parametrization for $G_E$ concludes an intense period of studying the $\gamma^\ast N \to \Delta(1232)$ quadrupole form factors at low $Q^2$, with the agreement between theory and data.

CP-violating top quark couplings at future linear e^+e^- colliders

We study the potential of future lepton colliders to probe violation of the CP symmetry in the top quark sector. In certain extensions of the Standard Model, such as the two-Higgs-doublet model (2HDM), sizeable anomalous top quark dipole moments can arise, which may be revealed by a precise measurement of top quark pair production. We present results from detailed Monte Carlo studies for the ILC at 500 hbox { GeV} and CLIC at 380 hbox { GeV} and use parton-level simulations to explore the potential of high-energy operation. We find that precise measurements in e^+e^- rightarrow tbar{t} production with subsequent decay to lepton plus jets final states can provide sufficient sensitivity to detect Higgs-boson-induced CP violation in a viable two-Higgs-doublet model. The potential of a linear e^+e^- collider to detect CP-violating electric and weak dipole form factors of the top quark exceeds the prospects of the HL-LHC by over an order of magnitude.

Nucleon Axial and Electromagnetic Form Factors

We present results for the isovector axial, induced pseudoscalar, electric, and magnetic form factors of the nucleon. The calculations were done using 2 + 1 + 1-flavor HISQ ensembles generated by the MILC collaboration with lattice spacings a ≈ 0.12, 0.09, 0.06 fm and pion masses Mπ ≈ 310, 220, 130 MeV. Excited-states contamination is controlled by using four-state fits to two-point correlators and by comparing two-versus three-states in three-point correlators. The Q2 behavior is analyzed using the model independent z-expansion and the dipole ansatz. Final results for the charge radii and magnetic moment are obtained using a simultaneous fit in Mπ, lattice spacing a and finite volume.

Structure of the Nucleon and its Excitations

The structure of the ground state nucleon and its finite-volume excitations are examined from three different perspectives. Using new techniques to extract the relativistic components of the nucleon wave function, the node structure of both the upper and lower components of the nucleon wave function are illustrated. A non-trivial role for gluonic components is manifest. In the second approach, the parity-expanded variational analysis (PEVA) technique is utilised to isolate states at finite momenta, enabling a novel examination of the electric and magnetic form factors of nucleon excitations. Here the magnetic form factors of low-lying odd-parity nucleons are particularly interesting. Finally, the structure of the nucleon spectrum is examined in a Hamiltonian effective field theory analysis incorporating recent lattice-QCD determinations of low-lying two-particle scattering-state energies in the finite volume. The Roper resonance of Nature is observed to originate from multi-particle coupled-channel interactions while the first radial excitation of the nucleon sits much higher at approximately 1.9 GeV.

Extraction of the neutron electric form factor from measurements of inclusive double spin asymmetries

Background: Measurements of the neutron charge form factor, GEn, are challenging because the neutron has no net charge. In addition, measurements of the neutron form factors must use nuclear targets which require accurately accounting for nuclear effects. Extracting GEn with different targets and techniques provides an important test of our handling of these effects. Purpose: The goal of the measurement was to use an inclusive asymmetry measurement technique to extract the neutron charge form factor at a four-momentum transfer of 1(GeV/c)2. This technique has very different systematic uncertainties than traditional exclusive measurements and thus serves as an independent check of whether nuclear effects have been taken into account correctly. Method: The inclusive quasielastic reaction 3He⃗(e⃗,e′) was measured at Jefferson Laboratory. The neutron electric form factor, GEn, was extracted at Q2=0.98(GeV/c)2 from ratios of electron-polarization asymmetries measured for two orthogonal target spin orientations. This Q2 is high enough that the sensitivity to GEn is not overwhelmed by the neutron magnetic contribution, and yet low enough that explicit neutron detection is not required to suppress pion production. Results: The neutron electric form factor, GEn, was determined to be 0.0414±0.0077(stat)±0.0022(syst), providing the first high-precision inclusive extraction of the neutron's charge form factor. Conclusions: The use of the inclusive quasielastic 3He⃗(e⃗,e′) with a four-momentum transfer near 1(GeV/c)2 has been used to provide a unique measurement of GEn. This new result provides a systematically independent validation of the exclusive extraction technique results and implies that the nuclear corrections are understood. This is contrary to the proton form factor where asymmetry and differential cross section measurements have been shown to have large systematic differences.Received 24 June 2017DOI:https://doi.org/10.1103/PhysRevC.96.065206©2017 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasPhotonuclear reactionsPhysical SystemsNeutronsPropertiesForm factorsNuclear PhysicsParticles & Fields

Sea quarks contribution to the nucleon magnetic moment and charge radius at the physical point

We report a comprehensive analysis of the light and strange disconnected-sea quarks contribution to the nucleon magnetic moment, charge radius, and the electric and magnetic form factors. The lattice QCD calculation includes ensembles across several lattice volumes and lattice spacings with one of the ensembles at the physical pion mass. We adopt a model-independent extrapolation of the nucleon magnetic moment and the charge radius. We have performed a simultaneous chiral, infinite volume, and continuum extrapolation in a global fit to calculate results in the continuum limit. We find that the combined light and strange disconnected-sea quarks contribution to the nucleon magnetic moment is ${\ensuremath{\mu}}_{M}(\mathrm{DI})=\ensuremath{-}0.022(11)(09)\text{ }\text{ }{\ensuremath{\mu}}_{N}$ and to the nucleon mean square charge radius is $⟨{r}^{2}{⟩}_{E}(\mathrm{DI})=\ensuremath{-}0.019(05)(05)\text{ }\text{ }{\mathrm{fm}}^{2}$ which is about $1/3$ of the difference between the $⟨{r}_{p}^{2}{⟩}_{E}$ of electron-proton scattering and that of a muonic atom and so cannot be ignored in obtaining the proton charge radius in the lattice QCD calculation. The most important outcome of this lattice QCD calculation is that while the combined light-sea and strange quarks contribution to the nucleon magnetic moment is small at about 1%, a negative 2.5(9)% contribution to the proton mean square charge radius and a relatively larger positive 16.3(6.1)% contribution to the neutron mean square charge radius come from the sea quarks in the nucleon. For the first time, by performing global fits, we also give predictions of the light and strange disconnected-sea quarks contributions to the nucleon electric and magnetic form factors at the physical point and in the continuum and infinite volume limits in the momentum transfer range of $0\ensuremath{\le}{Q}^{2}\ensuremath{\le}0.5\text{ }\text{ }{\mathrm{GeV}}^{2}$.

Charged current quasi elastic scattering of muon neutrino with nuclei

We present a study on the charge current quasi elastic scattering of $\nu_\mu$ from nucleon and nuclei which gives a charged muon in the final state. To describe nuclei, the Fermi Gas model has been used with proposed Pauli suppression factor. The diffuseness parameter of the Fermi distribution has been obtained using experimental data. We also investigate different parametrizations for electric and magnetic Sach's form factors of nucleons. Calculations have been made for CCQES total and differential cross sections for the cases of $\nu_{\mu}-N$, $\nu_{\mu}-^{12}C$ and $\nu_{\mu}-^{56}Fe$ scatterings and are compared with the data for different values of the axial mass. The present model gives excellent description of measured differential cross section for all the systems.

Lattice calculation of electric dipole moments and form factors of the nucleon

We analyze commonly used expressions for computing the nucleon electric dipole form factors (EDFF) $F_3$ and moments (EDM) on a lattice and find that they lead to spurious contributions from the Pauli form factor $F_2$ due to inadequate definition of these form factors when parity mixing of lattice nucleon fields is involved. Using chirally symmetric domain wall fermions, we calculate the proton and the neutron EDFF induced by the CP-violating quark chromo-EDM interaction using the corrected expression. In addition, we calculate the electric dipole moment of the neutron using background electric field that respects time translation invariance and boundary conditions, and find that it decidedly agrees with the new formula but not the old formula for $F_3$. Finally, we analyze some selected lattice results for the nucleon EDM and observe that after the correction is applied, they either agree with zero or are substantially reduced in magnitude, thus reconciling their difference from phenomenological estimates of the nucleon EDM.

The electromagnetic Sigma-to-Lambda hyperon transition form factors at low energies

.Using dispersion theory the low-energy electromagnetic form factors for the transition of a Sigma to a Lambda hyperon are related to the pion vector form factor. The additionally required input, i.e. the two-pion-Sigma-Lambda amplitudes are determined from relativistic next-to-leading-order (NLO) baryon chiral perturbation theory including the baryons from the octet and optionally from the decuplet. Pion rescattering is again taken into account by dispersion theory. It turns out that the inclusion of decuplet baryons is not an option but a necessity to obtain reasonable results. The electric transition form factor remains very small in the whole low-energy region. The magnetic transition form factor depends strongly on one not very well determined low-energy constant of the NLO Lagrangian. One obtains reasonable predictive power if this low-energy constant is determined from a measurement of the magnetic transition radius. Such a measurement can be performed at the future Facility for Antiproton and Ion Research (FAIR).

Measurement of two-photon exchange effect by comparing elastic e±p cross sections

[Background] The electromagnetic form factors of the proton measured by unpolarized and polarized electron scattering experiments show a significant disagreement that grows with the squared four momentum transfer ($Q^{2}$). Calculations have shown that the two measurements can be largely reconciled by accounting for the contributions of two-photon exchange (TPE). TPE effects are not typically included in the standard set of radiative corrections since theoretical calculations of the TPE effects are highly model dependent, and, until recently, no direct evidence of significant TPE effects has been observed. [Purpose] We measured the ratio of positron-proton to electron-proton elastic-scattering cross sections in order to determine the TPE contribution to elastic electron-proton scattering and thereby resolve the proton electric form factor discrepancy. [Methods] We produced a mixed simultaneous electron-positron beam in Jefferson Lab's Hall B by passing the 5.6 GeV primary electron beam through a radiator to produce a bremsstrahlung photon beam and then passing the photon beam through a convertor to produce electron/positron pairs. The mixed electron-positron (lepton) beam with useful energies from approximately 0.85 to 3.5 GeV then struck a 30-cm long liquid hydrogen (LH$_2$) target located within the CEBAF Large Acceptance Spectrometer (CLAS). By detecting both the scattered leptons and the recoiling protons we identified and reconstructed elastic scattering events and determined the incident lepton energy. A detailed description of the experiment is presented.

Electromagnetic properties of massive neutrinos in low-energy elastic neutrino-electron scattering

A thorough account of electromagnetic interactions of massive neutrinos in the theoretical formulation of low-energy elastic neutrino-electron scattering is given. The formalism of neutrino charge, magnetic, electric, and anapole form factors defined as matrices in the mass basis is employed under the assumption of three-neutrino mixing. The flavor change of neutrinos traveling from the source to the detector is taken into account and the role of the source-detector distance is inspected. The effects of neutrino flavor-transition millicharges and charge radii in the scattering experiments are pointed out.