Form Factors of Composite Systems by Generalized Wigner-Eckart Theorem for Poincar\'e group

The relativistic approach to electroweak properties of two-particle composite systems developed previously is generalized here to the case of nonzero spin. This approach is based on the instant form of relativistic Hamiltonian dynamics. A special mathematical technique is used for the parametrization of matrix elements of electroweak current operators in terms of form factors. The parametrization is a realization of the generalized Wigner--Eckart theorem on the Poincar\'e group, form factors are corresponding reduced matrix elements and they have the sense of distributions (generalized functions). The electroweak current matrix element satisfies the relativistic covariance conditions and in the case of electromagnetic current it also automatically satisfies the conservation law.Comment: Submitted to Theor. Math. Phy

Extraction of the neutron charge form factor from the charge form factor of deuteron

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 $Q^2 = 0$.Comment: LaTeX2e, 12 pages, 2 figures, tabl

Asymptotics of the deuteron form factors in the nucleon model and JLab experiments

Using the instant form dynamics of Poincar\'e invariant quantum mechanics and the modified relativistic impulse approximation proposed previously we calculate asymptotics of electromagnetic form factors for the deuteron considered as two--nucleon system. We show that today experiment on the elastic $ed$-scattering has reached asymptotic regime. The possible range of momentum transfer when the quark degrees of freedom could be seen in future JLab experiments is estimated. The explicit relation between the behavior of deuteron wave function at $r=0$ and the form factors asymptotics is obtained. The conditions on wave functions to give the asymptotics predicted by QCD and quark counting rules are formulated.Comment: 9 pages, 1 figur

Nonperturbative relativistic approach to pion form factor: predictions for future JLab experiments

Some predictions concerning possible results of the future JLab experiments on the pion form factor F_pi(Q^2) are made. The calculations exploit the method proposed previously by the authors and based on the instant-form Poincare invariant approach to pion considered as a quark-antiquark system. Long ago, this model has predicted with surprising accuracy the values of F_pi(Q^2) measured later in JLab experiment. The results are almost independent from the form of wave function. The pion mean square radius and the decay constant f_pi also agree with experimental values. The model gives power-like asymptotic behavior of F_pi(Q^2) at high momentum transfer in agreement with QCD predictions.Comment: 6 pages, 2 figures, revte

Asymptotic estimation of some multiple integrals and the electromagnetic deuteron form factors at high momentum transfer

A theorem about asymptotic estimation of multiple integral of a special type is proved for the case when the integrand peaks at the integration domain bound, but not at a point of extremum. Using this theorem the asymptotic expansion of the electromagnetic deuteron form factors at high momentum transfers is obtained in the framework of two-nucleon model in both nonrelativistic and relativistic impulse approximations. It is found that relativistic effects slow down the decrease of deuteron form factors and result in agreement between the relativistic asymptotics and experimental data at high momentum transfers.Comment: 16 pages, 1 figur