Form factor for a two-particle system within a relativistic quasipotential approach: Case of arbitrary masses and of a v
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CLEI Theory
Form Factor for a Two-Particle System within a Relativistic Quasipotential Approach: Case of Arbitrary Masses and of a Vector Current Yu. D. Chernichenko* Pavel Sukhoi State Technical University of Gomel, pr. Oktyabrya 48, Gomel, 246746 Belarus Received May 12, 2014
Abstract—A new relativistic form factor for a bound two-particle system was obtained for the case of a vector current. The present consideration was performed within the relativistic quasipotential approach based on the covariant Hamiltonian formulation of quantum field theory by going over to the threedimensional relativistic configuration representation for the case of interaction between two relativistic spinless particles of arbitrary mass. DOI: 10.1134/S1063778815010044
1. INTRODUCTION Investigation of elastic hadron form factors in the region of high momentum transfers made it possible to reveal regularities in their behavior [1]. Various pole models of vector-meson dominance (VMD) are widely used to describe the behavior of form factors. These models successfully reproduce the behavior of the pion form factor both in spacelike and in timelike regions [2], as well as the behavior of the nucleon form factor in the spacelike region [3]. However, an experimentally observed fast decrease in the electromagnetic proton form factor in the timelike region at high values of the squared 4-momentum transfer Q2 = −t according to the dipole law (in proportion to t−2 ) could not be explained within VMD models. This is because VMD models assume that a virtual photon incident to a nucleon “sees” only vector mesons (bound quark–antiquark states), but one probes the structure of the nucleon at short distances, where 4momentum transfers are quite high and where the motion of the quarks is quasifree (they possess an asymptotic freedom). A different approach to describing the behavior of electromagnetic form factors for baryons and nucleons in the timelike region near their thresholds was proposed in [4–6]. This approach is based on representing the baryon (nucleon) electromagnetic ¯ (N N ¯) form factor in the timelike region near the B B threshold in the form of the product of a factor that *
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corresponds to the singularity of the transition ampli¯ (N N ¯ ) threshold and a factor that tude far off the B B is responsible for strong final-state interaction. The latter determines the energy dependence of the form factor. However, the problem of a covariant description of form factors over the whole, not only asymptotic, energy region within a relativistic quark model that would take into account the difference in the quark masses has remained urgent to date. In order to solve this problem, it is necessary to know in more detail the dynamics of interacting quarks—in particular, to know the covariant wave functions for their relative motion. The relativistic covariant two-particle quasipotential equations derived by Logunov and Tavkhelidze [7] and by Kadyshevsky [8, 9] have been widely used to find the covariant wave functions fo
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