Mass spectrum of vector mesons and their leptonicdecay constants in the bilocal relativistic potential model
Abstract
A phenomenological model is developed in terms of bilocal meson fields in order to describe a vector meson and its leptonic decays. A new Salpeter equation for this particle and the SchwingerDyson equation allowing for the presence of an arbitrary potential and for a modification associated with the renormalization of the quark (antiquark ) wave function within the meson are given. An expression for the constant of the leptonic decay of the charged rho meson is obtained from an analysis of the decay process τ → ρν via parametrizing in it the hadronization of intermediate charged weak W bosons into a bilocal vector meson. The potential is chosen in the form of the sum of harmonicoscillator and Coulomb potentials, and the respective boundaryvalue problem is formulated. It is shown that the solutions to this problem describe both the mass spectrum of vector mesons and their leptonicdecay constants.
 Authors:
 Uzbek Academy of Sciences, Institute of Nuclear Physics (Uzbekistan)
 Publication Date:
 OSTI Identifier:
 22472457
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Physics of Atomic Nuclei; Journal Volume: 78; Journal Issue: 1; Other Information: Copyright (c) 2015 Pleiades Publishing, Ltd.; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; BOUNDARYVALUE PROBLEMS; COULOMB FIELD; HARMONIC OSCILLATORS; LEPTONIC DECAY; MASS SPECTRA; QUARKANTIQUARK INTERACTIONS; RELATIVISTIC RANGE; RENORMALIZATION; RHO770 MESONS; SCHWINGER FUNCTIONAL EQUATIONS; W MINUS BOSONS; W PLUS BOSONS; WAVE FUNCTIONS
Citation Formats
Ablakulov, Kh., Email: ablakulov@inp.uz, and Narzikulov, Z., Email: narzikulov@inp.uz. Mass spectrum of vector mesons and their leptonicdecay constants in the bilocal relativistic potential model. United States: N. p., 2015.
Web. doi:10.1134/S1063778814120023.
Ablakulov, Kh., Email: ablakulov@inp.uz, & Narzikulov, Z., Email: narzikulov@inp.uz. Mass spectrum of vector mesons and their leptonicdecay constants in the bilocal relativistic potential model. United States. doi:10.1134/S1063778814120023.
Ablakulov, Kh., Email: ablakulov@inp.uz, and Narzikulov, Z., Email: narzikulov@inp.uz. 2015.
"Mass spectrum of vector mesons and their leptonicdecay constants in the bilocal relativistic potential model". United States.
doi:10.1134/S1063778814120023.
@article{osti_22472457,
title = {Mass spectrum of vector mesons and their leptonicdecay constants in the bilocal relativistic potential model},
author = {Ablakulov, Kh., Email: ablakulov@inp.uz and Narzikulov, Z., Email: narzikulov@inp.uz},
abstractNote = {A phenomenological model is developed in terms of bilocal meson fields in order to describe a vector meson and its leptonic decays. A new Salpeter equation for this particle and the SchwingerDyson equation allowing for the presence of an arbitrary potential and for a modification associated with the renormalization of the quark (antiquark ) wave function within the meson are given. An expression for the constant of the leptonic decay of the charged rho meson is obtained from an analysis of the decay process τ → ρν via parametrizing in it the hadronization of intermediate charged weak W bosons into a bilocal vector meson. The potential is chosen in the form of the sum of harmonicoscillator and Coulomb potentials, and the respective boundaryvalue problem is formulated. It is shown that the solutions to this problem describe both the mass spectrum of vector mesons and their leptonicdecay constants.},
doi = {10.1134/S1063778814120023},
journal = {Physics of Atomic Nuclei},
number = 1,
volume = 78,
place = {United States},
year = 2015,
month = 1
}

Radiative leptonic decays of the pseudoscalar mesons are studied in the bilocal relativistic potential model. Partial and total widths of the pion decay are calculated. It is shown that, in the model under consideration, the decay widths can be determined by calculating the vector (f{sub v}) and axialvector (f{sub a}) form factors. These form factors can be found by jointly solving the Salpeter and SchwingerDyson equations with a specified interquark potential.

Mass spectrum and Regge trajectories of light vector mesons in the relativistic quark model
The mass spectrum and the Regge trajectories of vector mesons are calculated on the basis of the relativistic twoparticle quasipotential equation with a barrier potential that increases linearly with distance. 
Relativistic corrections to the mass spectrum of heavy mesons in the potential quark model
The mass spectrum of heavy mesons is calculated in the potential quark model using the most general form of the relativistic corrections due to singlegluon exchange in QCD. The nonrelativistic potential is approximated as the sum of a Coulomb part and a linear part. The parameters of the model are determined in the Psi and UPSILON families independently, taking into account the experimental mass splittings. The masses of the Phi, UPSILON, and (bcbar) states are calculated; in particular, M(2/sup 1/S/sub 0/ccbar) = 3593 + >5 MeV, M(1/sup 1/S/sub 0/bbbar) = 9421 + 5 MeV, and M(2/sup 1/S/sub 0/bbbar) = 9992more » 
Leptonic decay of light vector mesons in an independent quark model
Leptonic decay widths of light vector mesons are calculated in a framework based on the independent quark model with a scalarvector harmonic potential. Assuming a strong correlation to exist between the quarkantiquark momenta inside the meson, so as to make their total momentum identically zero in the centerofmass frame of the meson, we extract the quark and antiquark momentum distribution amplitudes from the bound quark eigenmode. Using the model parameters determined from earlier studies, we arrive at the leptonic decay widths of ([rho],[omega],[phi]) as (6.26 keV, 0.67 keV, 1.58 keV) which are in very good agreement with the respective experimentalmore »