Contributions Of Form Factors Research Articles

The determinant representation for quantum correlation functions of the sinh-Gordon model

We consider the quantum sinh-Gordon model in this paper. Form factors in this model were calculated by Mussardo and colleagues. We sum up all contributions of form factors and obtain a closed expression for a correlation function. This expression is a determinant of an integral operator. Similar determinant representations have been proven to be useful not only in the theory of correlation functions, but also in matrix models.

Two-point correlation functions in perturbed minimal models

Two point correlation functions of the off-critical primary fields \phi_{1, 1+s} are considered in the perturbed minimal models M_{2, 2N+3} + \phi_{1,3}. They are given as infinite series of form factor contributions. The form factors of \phi_{1, 1+s} are conjectured from the known results for those of \phi_{1,2} and \phi_{1,3}. The conjectured form factors are rewritten in the form which is convenient for summing up. The final expression of the two point functions is written as a determinant of an integral operator.

A small angle X-ray scattering study of sizes and shapes of poly(benzyl ether) dendrimer molecules

The structure of a series of poly(benzyl ether) dendrimers was derived from small angle X-ray scattering (SAXS) experiments of highly diluted solutions. The form factor contribution of the uncorrelated macromolecules contains information on their size and shape and reveals that they attain a globular structure. Electron distributions, calculated form the scattering data point towards an ellipsoidal shape with a rather uniform distribution of the electron density and hence the monomer subunits within the macromolecules.

A small angle X-ray scattering study of sizes and shapes of poly(benzyl ether) dendrimer molecules

The structure of a series of poly(benzyl ether) dendrimers was derived from small angle X-ray scattering (SAXS) experiments of highly diluted solutions. The form factor contribution of the uncorrelated macromolecules contains information on their size and shape and reveals that they attain a globular structure. Electron distributions, calculated form the scattering data point towards an ellipsoidal shape with a rather uniform distribution of the electron density and hence the monomer subunits within the macromolecules.

FENICE results and a first proposal for a new measurement of the nucleon form factors

The FENICE experiment was built in 1990 at the e + e − collider ADONE in Frascati to perform the first measurement of the electromagnetic form factor of the neutron in the time like-region, measuring the cross section of the reaction: e + e − → nn . The non-magnetic apparatus allowed the detection of nn and pp as well as multihadronic events. Results are presented on the first measurement of the neutron form factor from q 2 = 3.69 to q 2 = 5.95 for a total integrated luminosity of about 500 nb −1 , together with new results on the proton form factor in the same q 2 region and a new measurement of the total e + e − → hadrons cross section, close to the nucleon-antinucleon threshold. The neutron form factor turns out to be greater or equal than the proton one, and there are indications of a narrow vector resonance close to the nucleon-antinucleon threshold. The angular distribution of antiprotons and antineutrons has allowed to check the presence of the electric form factor contributions. The general behaviour of the neutron time-like form factor is rather unexpected. A proposal to perform another measurements using of an asymmetric e + e − collider is briefly discussed.

Potential model calculations of parity violation in proton-proton scattering.

The proton-proton parity-violating analyzing power is calculated at laboratory energies up to 1000 MeV using a parity-violating weak meson-exchange potential with form factors and coupling constants consistent with the nonrelativistic Bonn potential. A real distorted-wave Born-approximation formulation of the weak scattering amplitude is introduced using real standing waves with distortions by Coulomb and strong interactions. This formulation includes a new and simplified expression for the S matrix in terms of strong and real weak amplitudes. The form-factor contributions to the weak potential significantly reduce the overall magnitude of the analyzing power, but do not qualitatively affect the relative energy or angular dependence. Results using, alternatively, Paris, Reid soft-core, Hamada-Johnston, and pure Coulomb distorted waves with the same weak potential are compared. The angular and total analyzing powers are calculated with long-range Coulomb contributions for scattering and transmission experiments. The long-range Coulomb effects can be removed, leading to a reduced analyzing power \^A that depends only on short-range forces.

Lepton-induced weak interactions in nuclei in the 1 to 3 GeV range.

Differential cross sections are obtained for the reactions ${v}_{\ensuremath{\mu}}+^{12}\mathrm{C}\ensuremath{\rightarrow}^{12}\mathrm{N}+{\ensuremath{\mu}}^{\ensuremath{-}}$ and ${e}^{\ensuremath{-}}+^{12}\mathrm{C}\ensuremath{\rightarrow}^{12}\mathrm{B}+{v}_{e}$ for incoming lepton energies of 1 and 3 GeV. The contributions of individual form factors to the differential cross section are also found. A discussion of the utility of these processes for studying the weak nuclear current is given.

Angular dependence of light scattering structure coefficients for large anisotropic particles

The effects of particle and experimental geometries on the scattered electric field correlation function are studied in detail for a dilute solution of cylindrically symmetric anisotropic particles, in the Rayleigh–Debye approximation. Previous results for this system are simplified considerably through the use of the spherical harmonic coupling rule and the scattering angle and polarization dependence of the structure factors is computed explicitly. Expressions containing the particle form factor contributions to the first two dynamical term weighting coefficients are given and the interpretation of experiments which show the complexity of the anisotropy is discussed in detail.

Kaon-nucleus inelastic scattering

A theoretical investigation of kaon inelastic scattering is conducted for the specific reaction /sup 12/C(K/sup +/,K/sup +/')/sup 12/C* (J/sup ..pi../ = 2/sup +/,E/sub x/ = 4.43 MeV). The analysis utilizes the Kerman-McManus-Thaler multiple scattering formalism and the distorted wave impulse approximation. The distorting parameters are uniquely determined through the empirical K/sup +/-nucleon scattering amplitudes. Numerical results demonstrate a clear sensitivity to choice of amplitudes. The cross sections, calculated over a wide range of energies, display a slow variation. Fermi motion effects are found to be quite important at kaon lab kinetic energies below 300 MeV. The magnitude of the K/sup +/-nucleus elastic S matrix shows that the kaon is not strongly absorbed; however, cut-off calculations, which eliminate all internal form factor contributions, firmly establish the inelastic process is surface localized.

Polarization and asymmetry of protons in an annihilation process e? + e+ ? p + �p in the presence of weak neutral currents

The differential and total cross sections for annihilation of longitudinally polarized and transversely polarized electrons and positrons into pairs of longitudinally polarized protons and antiprotons are calculated in the center-of-mass system. The expressions obtained for the cross sections have electromagnetic, weak, and interference terms. It is shown that the existence of a weak current-current interaction (ēe) (¯pp) must lead for protons and antiprotons, emitted at an angle ®=90° to a nonzero degree of longitudinal polarization P(E) =1.3 and 36% for E=2.5 and 10 GeV and G=GF=10−5 M−2,to the presence of “forward-backward” asymmetry in the angular distribution of the protons A(E)=1 and 12% for E=2.5 and 10 GeV (the asymmetry exists even when all the particles are unpolarized), and to other effects which are absent in the case of a pure electromagnetic interaction. It is shown that in experiments with polarized particles the contributions of different form factors can be distinguished and studied separately.

Second class currents and broken SU(3)-symmetry

In the SU(3) limit, a second class, T-normal axial vector current, which transforms like an octet, can give rise to pseudotensor terms in the matrix elements for leptonic decays of baryons. With first order symmetry breaking, this second class current may generate pseudovector and pseudoscalar form factor contributions. It is an anti-hermitian current, but, even with SU(3) breaking, it does not need to disturb the chiral SU(2) × SU(2) algebra of charges.

Algorithms for the γ-algebra of electromagnetic form factors

We consider the γ-algebra arising in the calculation of contributions from any allowable vertex part to the electromagnetic form factors. Simple algorithms are established which enable any form factor contribution to be written down as a function of Chebyshev polynomials whose argument is P = 2 − q 2 , where q is the photon 4-momentum. These algorithms are particularly suitable for use in computer programmes for evaluating high-order vertex parts in perturbation theory.