An approach to the electroweak properties of two-particle composite systems is developed. The approach is based on the use of the instant form of relativistic Hamiltonian dynamics. The main feature of this approach is the method of construction of the matrix element of the electroweak current operator. The electroweak current matrix element satisfies the relativistic covariance conditions and in the case of the electromagnetic current also the conservation law automatically. The properties of the system as well as the approximations are formulated in terms of form factors. The approach makes it possible to formulate relativistic impulse approximation in such a way that the Lorentz covariance of the current is ensured. In the electromagnetic case the current conservation law is also ensured. Our approach gives good results for the pion electromagnetic form factor in the whole range of momentum transfers available for experiments at present time, as well as for the lepton decay constant of pions.

The charge form factor of the pion is calculated for momentum transfer range of Jefferson Lab experiments. The approach is based on the instant form of the relativistic Hamiltonian dynamics. It is shown that the form-factor dependence on the choice of the model for quark wave function in pion is weak, while the dependence on the constituent-quark mass is rather significant. It is possible to estimate the mass of constituent quark and the sum of anomalous magnetic moments of u-andd-quarks from the JLab experiments.PACS numbers: 12.39, 12.60.R, 13.40.G At present time the constituent quark model (CQM) is widely and successfully used for the description of hadron properties at low and intermediate energies [1][2][3][4][5][6][7][8][9][10][11][12][13]. The reasons for this are well known: first, CQM uses the physically adequate degrees of freedom; second, CQM describes nonperturbative effects. These facts give a possibility to use CQM for the investigation of the so called "soft" structure of hadrons, e.g. in exclusive processes, in contrast to QCD (see, e.g. [14]).The main feature of CQM versus QCD is the extraction of finite number of the most important degrees of freedom needed to describe the hadron. All dynamical effects of QCD are incorporated in CQM through the effective (constituent) quark mass and internal quark structure in terms of quark form factors. So, in the framework of CQM constituent quarks have all the material properties of free particles and interact with each other through the confinement potential. This means that constituent quark is characterized by an effective mass, a mean-square-radius (MSR) and an anomalous magnetic moment. Let us remark that the concept of extended constituent quarks also appears in some quantum field theory models, for example, in Nambu-Jona-Lasinio model with spontaneous chiral symmetry breaking [15]. In this context one can imagine that CQM is initiated by QCD. However, it is very important to remind ourselves that CQM is not a direct consequence of QCD, but a very * Electronic address: krutov@info.ssu.samara.ru † Electronic address: troitsky@theory.npi.msu.su successful phenomenological model [16]. For the description of electroweak properties it is necessary to take into account the relativistic effects, especially large in systems of light quarks. We will use the relativistic Hamiltonian dynamics (RHD) [17], which is one of approaches to describe relativistic properties of CQM.In the present paper we discuss the dependence of electromagnetic pion form factor on the internal quark structure. The interest to this problem is due particularly to a possible interpretation of current experiments in Jefferson Lab on the measurement of pion form factor [18] in the range of momentum transfer 0.5(GeV /c) 2 < Q 2 < 5(GeV /c) 2 . Using one of relativistic forms of CQM we obtain that pion form factor in this region of Q 2 depends strongly on the constituent quark mass, while the dependence on model quark interaction in pion is weak. This fact gives hope that it could be possi...

The relativistic approach to electroweak properties of twoparticle composite systems developed in Ref.[1] is generalized here to the case of nonzero spin. In developed technique the parametrization of matrix elements of electroweak current operators in terms of form factors is a realization of the Wigner-Eckart theorem on the Poincaré group and form factors are reduced matrix elements. The ρ meson charge form factor is calculated as an example. * Electronic address: krutov@ssu.samara.ru † Electronic address: troitsky@theory.sinp.msu.ru

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We present a unified model describing electroweak properties of the π and ρ mesons. Using a general method of relativistic parametrization of matrix elements of local operators, adjusted for the nondiagonal in total angular momentum case, we calculate the ρ-meson lepton-decay constant fρ using the same parameters of free constituent quarks that have ensured exclusively good results for the π meson previously. The only free parameter, characterising quark interactions, which include additional spin-spin contribution and hence differ from the π-meson case, is fixed by matching the decay constant to its experimental value. The mean square charge radius is calculated, r 2 ρ = (0.56 ± 0.04) fm 2 . This result verifies, for the ρ-meson case, the conjecture of equality between electromagnetic and strong radii of hadrons tested previously for proton, π and K mesons.

The asymptotics of pion charge form factor is obtained in the framework of relativistic Hamiltonian dynamics for the infinite value limit of momentum transfer and zero value limit of constituent-quark mass. It is shown that this asymptotics is the same as given by the perturbative QCD and is determined by relativistic kinematics only, being independent on the constituent quarks interaction in pion.

We derive an explicit analytical expression for the magnetic dipole moment of the ρ meson, μ ρ , in a relativistic constituent-quark model. We adopt our relativistic approach to composite systems, modified instant-form (mIF) relativistic quantum mechanics (RQM), that we used particularly to construct a unified π & ρ model [Phys. Rev. D 93, 036007 (2016)] describing electroweak properties of light mesons. This model provides a parameter-free calculation to give μ ρ ¼ 2.16 AE 0.03 ½e/2M ρ which is in accordance with the conventional experimental data. The magnetic, quadrupole, and charge form factors also are derived and presented. We consider the small uncertainty of our value of the magnetic moment as one of the undoubted advantages of the method. A comparison is made with recent lattice QCD results and previous calculations using a variety of methods.

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