Analytical calculations of ground and excited states of unequal mass heavy pseudoscalar and vector mesons mass spectra using Bethe-Salpeter formalism

Abstract

Considering the fact that, a wide range of variation in masses of various states of heavy pseudoscalar and vector mesons can be seen in different models and the experimental data on masses of many of these statesis not yet currently available, in this paper, we study the analytical calculation of heavy pseudoscalar and vector mesons mass spectra ( such as η c , B c , η b , J/ψ, B * c and Υ) and their corresponding wave functions in the framework of Bethe-Salpeter equation under the covariant instantaneous ansatz. The parameters of the framework were determined by a fit to the heavy pseudoscalar and vector mesons mass spectrum of ground states. These input parameters so fixed were found to give good agreements with data on mass spectra of ground and excited states of these mesons mass spectra.

Double Charmonium Productions in Electron-Positron Annihilation Using Bethe-Salpeter Approach

“…We had calculated recently the mass spectrum and various decays of ground and excited states of pseudoscalar and vector quarkonia in [18,19,20]. The same input parameters are employed in this calculation as in our recent works, given in table 1.…”

“…Our main aim in this paper was to study the cross section for double charmonium production in electron-positron collisions at center of mass energies, √ s = 10.6GeV., having successfully studied the mass spectrum and a range of low energy processes using an analytic treatment of 4 × 4 Bethe-Salpeter Equation (BSE) [18,19,20,21,22]. This is due to the fact any quark model model should successfully describe a range of processes-not only the mass spectra, and low energy hadronic decay constants/decay widths, but also the high energy production processes involving these hadrons, and all within a common dynamical framework, and with a single set of input parameters, that are calibrated to the mass spectrum.…”

“…In our recent works [17,18,19,20], we employed BSE under Covariant Instantaneous Ansatz, which is a Lorentz-invariant generalization of Instantaneous Approximation, to investigate the mass spectra and the transition amplitudes for various processes involving charmonium and bottomonium. The BSE framework using phenomenological potentials can give consistent theoretical predictions as more and more data are being accumulated.…”

“…We will use this framework for the calculation of cross section for the production of double charmonia, (J/ψ, η c ), (J/ψ, η c ), (ψ , η c ), and (ψ , η c ) in electron-positron annihilation that proceeds through a single virtual photon at center of mass energies, √ s = 10.6 GeV., where such problems do not enter in our previous papers on 4 × 4 BSE. [17,18,19,20,21,22].…”

“…and employing the heavy quark approximation on the propagators, the momenta k and q 1 can be written as, k ≈ 1 2 (P a +P b ) and q 1 ≈ P a + 1 2 P b , which leads to, k 2 ≈ s 4 and q 2 1 ≈ s 2 +m 2 c [10,11]. Then, with the above approximation and applying the definition of 3D BS wave function in [17,18,19,20] ψ(q a ) = i 2π M a dσΨ(P a , q a ) and ψ(q b ) = i 2π M b dσ b Ψ(P b , q b ), the double charmonium production BS amplitude, M 1 f i can be written in the instantaneous Bethe-Salpeter amplitude form as:…”