Spectrum for heavy quarkonia and mixture of the relevant wave functions within the framework of Bethe-Salpeter equation

Abstract

Considering the fact that some excited states of the heavy quarkonia (charmonium and bottomonium) are still missing in experimental observations and potential applications of the relevant wave functions of the bound states, we re-analyze the spectrum and the relevant wave functions of the heavy quarkonia within the framework of Bethe-Salpeter (B.S.) equation with a proper QCDinspired kernel. Such a kernel for the heavy quarkonia, relating to potential of the non-relativistic quark model, is instantaneous, so we call the corresponding B.S. equation as BS-In equation throughout the paper. Particularly, a new way to solve the B.S. equation, which is different from the traditional ones, is proposed here, and with it not only the known spectrum for the heavy quarkonia is re-generated, but also an important issue is brought in, i.e., the obtained solutions of the equation 'automatically' include the 'fine', 'hyperfine' splittings and the wave function mixture, such as S -D wave mixing in J PC = 1 −− states, P-F wave mixing in J PC = 2 ++ states for charmonium, bottomonium etc. It is pointed out that the best place to test the wave mixture probably is at Z-factory (e + e − collider running at Z-boson pole with extremely high luminosity). Bethe-Salpeter equation, heavy quarkonium, spectrum, bound state wave-mixing

The study of rare $ {B_c}\to D_{s,d}^{{\left( * \right)}}l\overline{l} $ decays

“…As shown in ref. [45], the mass spectra with these input constituent quark masses are in good agreement with the experimental data. Thus, this set of numerical values is adopted in this paper.…”

Radiative Decay Widths of Ground and Excited States of Vector Charmonium and Bottomonium

“…On the contrary all the other 4×4 approaches adopt a purely numerical approach of solving the coupled set of Salpeter equations, which may enhance the numerical accuracy, but this is at the expense of a deeper understanding of the spectral problem. We further wish to mention that the correctness of our approximations can be judged by the fact that our plots of wave functions obtained analytically for various states of and quarkonia [21] are very similar to the corresponding plots of wave functions of various states of these quarkonia obtained by purely numerical approach in [13].…”

“…(21) of [21]). Solving them simultaneously leads to (13) of present paper (which is Eq. (23) in [21]), written in terms of .…”

“…As regards the dynamical framework, to investigate these properties is concerned; many nonperturbative approaches, such as lattice QCD [5], chiral perturbation theory [6], QCD sum rules [7], heavy-quark effective theory [8], NRQCD [9], dynamical-equation based approaches like SchwingerDyson equation and Bethe-Salpeter equation (BSE) [10][11][12][13][14][15], and potential models [16] have been proposed to deal with the long distance property of QCD.…”

The rare semi-leptonic B c decays involving orbitally excited final mesons

“…The CPPs can be found in ref. [57]. The masses of the constituent quarks are taken as m b = 4.96 GeV, m c = 1.62 GeV, m s = 0.5 GeV and m d = 0.311 GeV [47].…”