Relativistic instant-form approach to the structure of two-body composite systems

Abstract

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.

Form factors in RQM approaches: Constraints from space-time translations

“…Concerning the application of dispersion relations to the calculation of the charge form factor, F 1 (Q 2 ), we refer to ref. [12] for details. It is noticed that the expression so obtained assumes current conservation and the simplest one-body current, < p i |J µ |p f >∝ (p i + p f ) µ .…”

“…Besides the instant-, front-and point-form approaches, a dispersion-relation based approach has been considered in the literature, see for instance works by Anisovich et al [11] or by Krutov and Troitsky [12] and references therein. At some point, this approach should evidence some relationship with RQM approaches.…”

Correspondence between QCD sum rules and constituent quark models

“…Among them: (i) hadron spectroscopy where mesons and baryons spectra may be well described in the relativistic constituent quark model [1]; (ii) high-energy hadron-hadron and hadron-nucleus scattering at small and intermediate momentum transfers where momentum distributions of secondary particles are well described assuming that mesons and nucleons are bound states of two and three constituent quarks, respectively [2]; (iii) photon-hadron scattering at small momentum transfers where the observables speak in favor of the presence of few extended objects inside hadrons [3]; (iv) exclusive processes at small and intermediate momentum transfers where the constituent quark picture has been successfully applied to the calculation of elastic and transition form factors. Indeed, various models based on the notion of constituent quarks can be found in the literature, for instance the dispersion approach [4,5], the quasipotential approach [6], light-front [7,8], instant-form [9] and pointform [10] quark models. For more details we refer to the review [11].…”

Poincaré-invariant constituent quark model for light mesons: capabilities and constraints

“…In Ref. [40] we compared the predictions for analytic properties of the pion form factor in the complex plane of transferred momenta t = −Q 2 that follow from QFT general principles with those obtained by the analytic continuation of the form factor integral representation (14) in the spacelike domain derived in the framework of the instant form of RQM [13]. It follows from the QFT microcausality condition that the pion form factor is an analytic function in the complex plane of the parameter t with a cut running from 4m 2 π to ∞, where m π is the pion mass (see, e.g., [41] and the references therein).…”

“…The developed procedure can be applied to the construction of the electromagnetic current twoquark system. The following integral representation for the pion form factor in the MIA (see, e.g., [1,12,13]) holds:…”