Charge Form Factor Research Articles

Gravitational and higher-order form factors of the pion in chiral quark models

The gravitational form factor of the pion is evaluated in two chiral quark models and confronted with the recent full-QCD lattice data. We find good agreement for the case of the spectral quark model, which builds in the vector-meson dominance for the charge form factor. We derive a simple relation between the gravitational and electromagnetic form factors, holding in the considered quark models in the chiral limit. The relation implies that the gravitational mean squared radius is half the electromagnetic one. We also analyze higher-order quark generalized form factors of the pion, related to higher moments in the symmetric Bjorken X variable of the generalized parton distribution functions, and discuss their perturbative QCD evolution, which is needed to relate the quark-model predictions to the lattice data. The values of the higher-order quark form factors at t=0, computed on the lattice, also agree with our quark-model results within the statistical and method uncertainties.

Charged pion form factor betweenQ2=0.60and2.45 GeV2. II. Determination of, and results for, the pion form factor

The charged pion form factor, Fπ(Q2), is an important quantity that can be used to advance our knowledge of hadronic structure. However, the extraction of Fπ from data requires a model of the 1H(e,e'π+)n reaction and thus is inherently model dependent. Therefore, a detailed description of the extraction of the charged pion form factor from electroproduction data obtained recently at Jefferson Lab is presented, with particular focus given to the dominant uncertainties in this procedure. Results for Fπ are presented for Q2=0.60−2.45 GeV2. Above Q2=1.5 GeV2, the Fπ values are systematically below the monopole parametrization that describes the low Q2 data used to determine the pion charge radius. The pion form factor can be calculated in a wide variety of theoretical approaches, and the experimental results are compared to a number of calculations. This comparison is helpful in understanding the role of soft versus hard contributions to hadronic structure in the intermediate Q2 regime.4 MoreReceived 11 July 2008DOI:https://doi.org/10.1103/PhysRevC.78.045203©2008 American Physical Society

Charged pion form factor betweenQ2=0.60and 2.45GeV2. I. Measurements of the cross section for the1H(e,e'π+)nreaction

Cross sections for the reaction 1H(e,e'π+)n were measured in Hall C at Thomas Jefferson National Accelerator Facility (JLab) using the high-intensity Continuous Electron Beam Accelerator Facility (CEBAF) to determine the charged pion form factor. Data were taken for central four-momentum transfers ranging from Q2=0.60 to 2.45 GeV2 at an invariant mass of the virtual photon-nucleon system of W=1.95 and 2.22 GeV. The measured cross sections were separated into the four structure functions σL,σT,σLT, and σTT. The various parts of the experimental setup and the analysis steps are described in detail, including the calibrations and systematic studies, which were needed to obtain high-precision results. The different types of systematic uncertainties are also discussed. The results for the separated cross sections as a function of the Mandelstam variable t at the different values of Q2 are presented. Some global features of the data are discussed, and the data are compared with the results of some model calculations for the reaction 1H(e,e'π+)n.16 MoreReceived 11 July 2008DOI:https://doi.org/10.1103/PhysRevC.78.045202©2008 American Physical Society

Charge Form Factor of the Neutron at Low Momentum Transfer from theH→2(e→,e′n)H1Reaction

We report new measurements of the neutron charge form factor at low momentum transfer using quasielastic electrodisintegration of the deuteron. Longitudinally polarized electrons at an energy of 850 MeV were scattered from an isotopically pure, highly polarized deuterium gas target. The scattered electrons and coincident neutrons were measured by the Bates Large Acceptance Spectrometer Toroid (BLAST) detector. The neutron form factor ratio GEn/GMn was extracted from the beam-target vector asymmetry AedV at four-momentum transfers Q2=0.14, 0.20, 0.29, and 0.42 (GeV/c)2.Received 26 March 2008DOI:https://doi.org/10.1103/PhysRevLett.101.042501©2008 American Physical Society

Charge form factor and cluster structure of the 6Li nucleus

Abstract The charge form factor of the 6Li nucleus is considered on the basis of its cluster structure. The charge density of 6Li is presented as a superposition of two terms. One of them is a folded density and the second one is a sum of the 4He and deuteron densities. Using the available experimental data for 4He and deuteron charge form factors, a satisfactory agreement of the calculations within the suggested scheme is obtained with the experimental data for the charge form factor of 6Li, including those in the region of large transferred momenta.

Deuteron form factors in chiral effective theory: Regulator-independent results and the role of two-pion exchange

We evaluate the deuteron charge, quadrupole, and magnetic form factors using wave functions obtained from chiral effective theory ($\chi$ET) when the potential includes one-pion exchange, chiral two-pion exchange, and genuine contact interactions. We study the manner in which the results for form factors behave as the regulator is removed from the $\chi$ET calculation, and compare co-ordinate- and momentum-space approaches. We show that, for both the LO and NNLO chiral potential, results obtained by imposing boundary conditions in co-ordinate space at $r=0$ are equivalent to the $\Lambda \to \infty$ limit of momentum-space calculations. The regulator-independent predictions for deuteron form factors that result from taking the $\Lambda \to \infty$ limit using the LO $\chi$ET potential are in reasonable agreement with data up to momentum transfers of order 600 MeV, provided that phenomenological information for nucleon structure is employed. In this range the use of the NNLO $\chi$ET potential results in only small changes to the LO predictions, and it improves the description of the zero of the charge form factor.

Gravitational form factors of vector mesons in an AdS/QCD model

We calculate gravitational form factors of vector mesons using a holographic model of QCD. These provide restrictions on the generalized parton distributions of vector mesons, via the sum rules connecting stress tensor form factors to generalized parton distributions. We concentrate on the traceless part of the stress tensor, which suffices to fix the momentum and angular momentum sum rules. The vector mesons appear noticeably more compact measured by the gravitational form factors than by the charge form factor.

Sea-quark effects in the pion charge form factor

It is shown that the data on the pion charge form factor admit the possibility for a substantial sea-quark component in the pion wave function. If the charge form factor is calculated with instant form kinematics in a constituent quark model that is extended to include explicit $(q\overline{q}){}^{2}$ components in the pion wave function, that component will give the dominant contribution to the calculated ${\ensuremath{\pi}}^{+}$ charge form factor at large values of momentum transfer. The present experimental values ${Q}^{2}$ can be described fairly well with $(q\overline{q}){}^{2}$ component admixtures of up to 50%. The sensitivity of the calculated ${\ensuremath{\pi}}^{+}$ charge form factor to whether one of the quarks or one of the antiquarks is taken to be in the $P$ state is small.

Recent results from NA48/2 on Ke4 and K3 π decays, interpretation in terms of ππ scattering lengths

New results from the NA48/2 experiment at the CERN/SPS are presented. Large samples of Ke4 decays have been collected in 2003 and 2004 in the charged ( K ± → π + π − e ± ν ) and neutral ( K ± → π 0 π 0 e ± ν ) modes. Form factors and Branching fraction measurements are reported. The ππ scattering lengths a 0 0 and a 0 2 can be extracted from the charged Ke4 form factor δ and from the K3 π cusp in the M 00 2 distribution.

Tau anomalous magnetic moment form factor at super B/flavor factories

The proposed high-luminosity B/flavor factories offer new opportunities for the improved determination of the fundamental physical parameters of standard heavy leptons. Compared to the electron or the muon case, the magnetic properties of the τ lepton are largely unexplored. We show that the electromagnetic properties of the τ, and in particular its magnetic form factor, may be measured competitively in these facilities, using unpolarized or polarized electron beams. Various observables of the τ's produced on top of the ϒ resonances, such as cross-section and normal polarization for unpolarized electrons or longitudinal and transverse asymmetries for polarized beams, can be combined in order to increase the sensitivity on the magnetic moment form factor. In the case of polarized electrons, we identify a special combination of transverse and longitudinal τ polarizations able to disentangle this anomalous magnetic form factor from both the charge form factor and the interference with the Z-mediating amplitude. For an integrated luminosity of 15 × 10 18 b −1 one could achieve a sensitivity of about 10 −6, which is several orders of magnitude below any other existing high- or low-energy bound on the magnetic moment. Thus one may obtain a QED test of this fundamental quantity to a few % precision.

Study of the isotonic shifts of charge form factor for the light proton-rich nuclei

Charge form factors of elastic electron scattering on light proton-rich nuclei on the N = 8 , 10, 20, and 28 isotonic chains are calculated using the relativistic eikonal approximation with the charge density distributions from the RMF model. The results show that the occupation of the 2 s 1 / 2 state by protons has a great influence on the charge density distribution and consequently on the charge form factor. The results can be useful for the study of behavior of the valence-proton wave functions for such light proton-rich nuclei as can be considered as a cluster plus proton(s), and thus the proton-halo phenomenon. And also the results can be used as a very good test of the single-particle motion determined by the mean field model.

Nucleon form factors and the BLAST experiment

Measurements of the charge and magnetic form factors of the nucleon present a sensitive test of nucleon models and QCD-inspired theories. A precise knowledge of the neutron form factors at low Q 2 is also essential to reduce the systematic errors of parity-violation experiments. At the MIT-Bates Linear Accelerator Center, the nucleon form factors have been measured by means of scattering of polarized electrons from vector-polarized hydrogen and deuterium. The experiment used the longitudinally polarized stored electron beam of the MIT-Bates South Hall Ring along with an isotopically pure, highly vector-polarized internal atomic hydrogen and deuterium target provided by an atomic beam source. The measurements have been carried out with the symmetric Bates Large-Acceptance Spectrometer Toroid (BLAST) with enhanced neutron detection capability.

Determination of the pion charge form factor forQ2=0.60–1.60 GeV2

The data analysis for the reaction H(e,e' pi^+)n, which was used to determine values for the charged pion form factor Fpi for values of Q^2=0.6-1.6 GeV^2, has been repeated with careful inspection of all steps and special attention to systematic uncertainties. Also the method used to extract Fpi from the measured longitudinal cross section was critically reconsidered. Final values for the separated longitudinal and transverse cross sections and the extracted values of Fpi are presented.

Determination of the Pion Charge Form Factor atQ2=1.60and2.45 (GeV/c)2

The 1H(e,e'pi+)n cross section was measured at four-momentum transfers of Q2=1.60 and 2.45 GeV2 at an invariant mass of the photon nucleon system of W=2.22 GeV. The charged pion form factor (F(pi)) was extracted from the data by comparing the separated longitudinal pion electroproduction cross section to a Regge model prediction in which F(pi) is a free parameter. The results indicate that the pion form factor deviates from the charge-radius constrained monopole form at these values of Q2 by one sigma, but is still far from its perturbative quantum chromodynamics prediction.

Cross Sections of Elastic Electron and Positron Scatteringfrom Proton-Rich Nuclei

We investigate the cross sections of the elastic electron or positronscattering from 208Pb, 12C, 12,16O and 28,32S by therelativistic partial-wave expansion method using the static chargedensity distribution from the self-consistent relativistic mean fieldmodel and also calculate the charge form factor for 12,16O and28,32S. The numerical results are compared with the available data.Calculations indicate that the extended charge densitydistributions of 12O and 28S have observable effects onthe cross sections of the electron or positron scattering as wellas the charge form factors.

Electromagnetic Properties of S11 States in a Light Cone QuarkModel

Using relativistic spin-flavor wave functions of a Lorentz-covariantlight cone quark model, we calculate the electromagnetic formfactors of two S11 resonances, N(1535) and N(1650), and thehelicity amplitudes A1/2 and S1/2 for electroexcitation ofthe S11 resonances from the nucleon. The electromagnetic formfactors of these S11 resonances are found to be similar tothose of the nucleon in shape, while the charge form factor ofneutral N(1650) is nearly zero. The relative peak height of theS11 charge form factors is controlled by the mixing anglecommon to both resonance wave functions. As in most quark models,there is a systematic overestimate of A1/2p in both N(1535)and N(1650) cases at the photon point. A sizeable S1/2 forall cases is produced as suggested by experiments.

The α particle as a canonically quantized multiskyrmion

The rational map approximation to the solution to the SU(2) Skyrme model with baryon number $B=4$ is canonically quantized. The quantization procedure leads to anomalous breaking of the chiral symmetry, and exponential fall-off of the energy density of the soliton at large distances. The model is extended to SU(2) representations of arbitrary dimension. These soliton solutions capture the double node feature of the empirical \ensuremath{\alpha} particle charge form factor, but as expected lead to a too compact matter distribution. Comparison to phenomenology indicates a preference for the fundamental representation.

Deuteron structure and diffractive deuteron-nucleus interaction

A nonrelativistic deuteron wave function involving the D-wave state and having a correct asymptotic behavior is constructed on the basis of the experimentally measured deuteron charge form factor GC(q) and deuteron structure function A(q). The differential cross section for elastic deuteron-nucleus scattering is calculated by using this wave function and is found to agree with experimental data at an energy of 110 MeV. Integrated cross sections for various processes involving deuteron-nucleus interactions are also calculated. The distribution in the emission angle of the center of mass of the neutron-proton system produced in the diffractive dissociation of 110-MeV deuterons in the field of 208Pb nuclei is obtained.

Electromagnetic form factors of the nucleon

Elastic form factors are of fundamental importance for the understanding of microscopic spatial structures. In case of the proton and the neutron, charge and magnetic form factors can be studied in elastic electron scattering. Techniques to accelerate polarised continuous electron beams, the availability of polarised targets as well as modern concepts and instrumentation for coincidence experiments and recoil polarimetry had an enormous impact on these measurements. The developments and experiments at the Mainz Microtron MAMI will be discussed in a general context.

Study of the branching ratio and charge asymmetry for the decay [formula omitted] with the KLOE detector

Among some 400 million KSKL pairs produced in e+e− annihilations at DAΦNE, ∼6500 each of KS→π+e−ν¯ and KS→π−e+ν decays have been observed with the KLOE detector. From these, the ratio Γ(KS→πeν)/Γ(KS→π+π−)=(10.19±0.13)×10−4 is obtained, improving the accuracy on BR(KS→πeν) by a factor of four and providing the most precise test of the ΔS=ΔQ rule. From the partial width Γ(KS→πeν), a value for f+K0(0)×Vus is obtained that is in agreement with unitarity of the quark-mixing matrix. The lepton charge asymmetry AS=(1.5±9.6stat±2.9syst)×10−3 is compatible with the requirements of CPT invariance. The form-factor slope agrees with recent results from semileptonic KL and K+ decays. These are the first measurements of the charge asymmetry and form-factor slope for semileptonic KS decays.