Nucleon form factors in a projected chiral soliton model with dynamical confinement

We calculate nucleon form factors in the framework of a chiral chromodielectric model. The model state describing the nucleon is an angular momentum and isospin eigenstate with obtained by means of Peierls-Yoccoz projection from the hedgehog. We present results for the electromagnetic form factors and also for the axial form factors of the nucleon. There is a fairly good agreement with the data for small momentum transfers. For high momentum transfers (i.e. q² > 0.1 GeV² the agreement becomes poorer. As a general rule the calculated form factors fall too rapidly.     

NUCLEON PROPERTIES IN A QUARK BAG MODEL WITH WOODS-SAXON TYPE CONFINING POTENTIAL

A quark bag model with Woods-Saxon type confining potential is suggested. This model is used to examine three well-nown characteristic quantities of the nucleon and the proton electromagnetic form factors are evaluated by considering the quark core contributions. It is found that our model employing a confinement of W-S potential can improve the fit with the experimental values and can give good results for the form factors.     

Form factors in the Bullough-Dodd related models: The Ising model in a magnetic field

A particular modification of the free-field representation of the form factors in the Bullough-Dodd model is considered. The two-particles minimal form factors are excluded from the construction. As a consequence, a convenient representation for the multiparticle form factors has been obtained, recurrence relations between them have been established, and their properties have been studied. The proposed construction is used to obtain the free-field representation of the lightest particles form factors in the Φ_{1, 2} perturbed minimal models. The Ising model in a magnetic field is considered as a significant example. The results obtained in the framework of the proposed free-field representation are in agreement with the corresponding results obtained by solving the bootstrap equations.     

Bag-model form factors and Hartree-Fock approximation to the σωπ model

We evaluate form factors for the scattering ofσ, ω andπ mesons from nucleons described by the MIT bag model. These form factors are then written covariantly and used for nuclear matter in the Hartree-Fock approximation to theσω model of quantum hadrodynamics with pions. For fixed parameters (meson couplings and masses) the inclusion of these form factors results in more binding at a higher saturation density. After refitting the parameters to reproduce the empirical saturation properties, the result is very close to that without form factors.     

Electromagnetic properties of baryons in a relativistic quark model

Results on electromagnetic form factors of the nucleon and photon transition form factors of non-strange baryon resonances calculated in a relativistically covariant quark model based on the Bethe-Salpeter equation are presented. The relevance of the instanton-induced quark interaction on these properties is discussed.Received: 30 September 2002, Published online: 22 October 2003PACS: 11.10.St Bound and unstable states; Bethe-Salpeter equations - 12.39.Ki Relativistic quark model - 12.40.Yx Hadron mass models and calculations - 13.40.Gp Electromagnetic form factors     

Form factors in finite volume I: Form factor bootstrap and truncated conformal space

We describe the volume dependence of matrix elements of local fields to all orders in inverse powers of the volume (i.e., only neglecting contributions that decay exponentially with volume). Using the scaling Lee–Yang model and the Ising model in a magnetic field as testing ground, we compare them to matrix elements extracted in finite volume using truncated conformal space approach to exact form factors obtained using the bootstrap method. We obtain solid confirmation for the form factor bootstrap, which is different from all previously available tests in that it is a non-perturbative and direct comparison of exact form factors to multi-particle matrix elements of local operators, computed from the Hamiltonian formulation of the quantum field theory. We also demonstrate that combining form factor bootstrap and truncated conformal space is an effective method for evaluating finite volume form factors in integrable field theories over the whole range in volume.     

Exact form factors in integrable quantum field theories: the sine-Gordon model (II)

A general model independent approach using the ‘off-shell Bethe Ansatz’ is presented to obtain an integral representation of generalized form factors. The general techniques are applied to the quantum sine-Gordon model alias the massive Thirring model. Exact expressions of all matrix elements are obtained for several local operators. In particular soliton form factors of charge-less operators as for example all higher currents are investigated. It turns out that the various local operators correspond to specific scalar functions called p-functions. The identification of the local operators is performed. In particular the exact results are checked with Feynman graph expansion and full agreement is found. Furthermore all eigenvalues of the infinitely many conserved charges are calculated and the results agree with what is expected from the classical case. Within the frame work of integrable quantum field theories a general model independent ‘crossing’ formula is derived. Furthermore the ‘bound state intertwiners’ are introduced and the bound state form factors are investigated. The general results are again applied to the sine-Gordon model. The integrations are performed and in particular for the lowest breathers a simple formula for generalized form factors is obtained.     

One-loop generated anomalous gauge couplings

We compute, at one loop, the CP-violating anomalous trilinear gauge-boson form factors which couple theW (or theZ) to the photon and theZ. In order to see which form factors are generated by which types of underlying interactions, we work with as general an underlying model as is possible. After identifying which form factors can arise at one loop in a completely general renormalizable model of spin-half and spin-zero particles, we provide explicit formulae for the induced form factors in a very broad class of such models. Our results include some previous calculations as special cases, and we identify errors in some of these.     

Weak form factors for semileptonic octet baryon decays in the chiral quark model

We study the weak vector and axial-vector form factors of first- and second-class currents for the semileptonic octet baryon decays in the spirit of the chiral quark model. Our results for the weak magnetism form factors are consistent with the conserved vector current (CVC) results. The induced pseudotensor form factors, which are highly model dependent, are small. The overall performance of the chiral quark model is quite good and in general agreement with existing experimental data. Received: 9 March 1998 / Published online: 12 August 1998     

Ising Correlations and Elliptic Determinants

Correlation functions of the two-dimensional Ising model on the periodic lattice can be expressed in terms of form factors—matrix elements of the spin operator in the basis of common eigenstates of the transfer matrix and translation operator. Free-fermion structure of the model implies that any multiparticle form factor is given by the pfaffian of a matrix constructed from the two-particle ones. Crossed two-particle form factors can be obtained by inverting a block of the matrix of linear transformation induced on fermions by the spin conjugation. We show that the corresponding matrix is of elliptic Cauchy type and use this observation to solve the inversion problem explicitly. Non-crossed two-particle form factors are then obtained using theta functional interpolation formulas. This gives a new simple proof of the factorized formulas for periodic Ising form factors, conjectured by A. Bugrij and one of the authors.     

Parity Violation in Electron Quasi-Elastic Scattering

Parity violating electron scattering on a nucleus in the quasi-elastic region is investigated within a relativistic single particle model from ²⁰⁸Pb and with the incident electron energy up to 1 GeV. We discuss the effect of nucleon electromagnetic form factors by comparing the standard Sachs form factors with the parameterized form recently adjusted to the world data. The effect of the strangeness is also investigated through the recent results of the strangeness form factors, and we separately calculate the asymmetries of longitudinal and transverse response functions.     

Exact form factors in integrable quantum field theories: the sine-Gordon model

We provide detailed arguments on how to derive properties of generalized form factors, originally proposed by one of the authors (M.K.) and Weisz twenty years ago, solely based on the assumption of ‘maximal analyticity” and the validity of the LSZ reduction formalism. These properties constitute consistency equations which allow the explicit evaluation of the n-particle form factors once the scattering matrix is known. The equations give rise to a matrix Riemann-Hilbert problem. Exploiting the “off-shell” Bethe ansatz we propose a general formula for form factors for an odd number of particles. For the sine-Gordon model alias the massive Thirring model we exemplify the general solution for several operators. In particular we calculate the three-particle form factor of the soliton field, carry out a consistency check against the Thirring model perturbation theory and thus confirm the general formalism.     

Scaling laws in high-energy electron-nuclear scattering

The approximate scaling behavior suggested by recent measurements of electron scattering form factors and inelastic structure functions of few-body nuclei (mass 2, 3, 4) is discussed in a relativistic impulse approximation model. The model is a straightforward extension incorporating spin of a nucleon parton model introduced in recent works. We present results for electric and magnetic form factors as well as inelastic structure functions near threshold. The important corrections to scaling which are present in the preasymptotic regions are found to be well accounted for by the type of binding effects included in the phenomenologically constructed infinite-momentum frame nuclear wave functions. While predicted form factors are very sensitive to the parameters in the wave functions it does not appear possible to associate unambiguous dynamical meaning to these parameters. We find that spin effects bring significant and useful corrections.     

A QCD-Inspired Model for the Deuteron Form Factors in the Intermediate-Q2 Region

Based on a perturbative QCD analysis of the deuteron form factors a QCD-inspired model is suggested. The contributions of helicity-flip matrix elements to the deuteron form factors are discussed. Our numerical results are consistent with the data in the intermediate-Q² region.     

6Li electromagnetic form factors and phenomenological cluster models

The longitudinal form factors of the ground and 2.18 MeV (3⁺, T = 0) states, and the transverse form factors of the 3.56 MeV (0⁺, T = 1) and 5.37 MeV (2⁺, T = 1) states of ⁶Li are compared with the predictions based on fully antisymmetrized α-d and t-τ cluster models. The longitudinal form factors are adequately described by the α-d model, but the transverse form factors seem to be more consistent with a t-τ model which is close to the shell-model limit. Estimates are made for the ground state t and α spectroscopic factors. The 3.56 MeV M1 transition current density is calculated for both models and compared with experiment.     

Form factors in the presence of integrable defects

Form factor axioms are derived in two dimensional integrable defect theories for matrix elements of operators localized both in the bulk and on the defect. The form factors of bulk operators are expressed in terms of the bulk form factors and the transmission factor. The structure of the form factors of defect operators is established in general, and explicitly calculated in particular, for the free boson and for some operator of the Lee–Yang model. Fusion method is also presented to generate boundary form factor solutions for a fused boundary from the known unfused ones.     

Breather boundary form factors in sine-Gordon theory

A previously conjectured set of exact form factors of boundary exponential operators in the sinh-Gordon model is tested against numerical results from boundary truncated conformal space approach in boundary sine-Gordon theory, related by analytic continuation to sinh-Gordon model. We find that the numerical data strongly support the validity of the form factors themselves; however, we also report a discrepancy in the case of diagonal matrix elements, which remains unresolved for the time being.     

Elastic vN and ̄vN scattering and strange form factors of the nucleons

Elastic scattering of neutrinos and antineutrinos on nucleons is considered. It is shown that the measurement of the neutrino-antineutrino asymmetry would allow to obtain model independent information on the strange axial and vector form factors. The ratio of the magnetic form factors of the proton and neutron, on which the asymmetry depends, is investigated in detail. The asymmetry is calculated under different assumptions on the behavior of the strange vector and axial form factors.     

Isovector form factors and the rho-prime

A simple but successful pole model for the low q² behaviour of the pion, ΔNγ and nucleon isovector form factors is given, using the Dirac form factors in the latter case. The rho-prime required decouples completely from charge form factors, so that its only two body decay mode is ωπ.