Spectrum for Heavy Quankonia 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) 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 QCD-inspired kernel. Such a kernel for the heavy quarkonia, relating to potential of 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 and 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).

26 pages, 8 figures

References in corpus (2)

• Decay constants of $P$-wave mesons
• Production of a Heavy Quarkonium with a Photon or via ISR at $Z$ Peak in $e^{+}{e}^{-}$ Collider

Cited by in corpus (9)

• The mass spectrum and wave functions of the $B_c$ system
• Two-Body Strong Decay of the 2P and 3P Charmonium states
• The Strong Decays of X(3940) and X(4160)
• The electromagnetic decays of $X(3823)$ as the ${\psi }_2(1^3{D}_2)$ state and its radial excited states
• Coherent photoproduction of heavy quarkonia on nuclei
• Partial wave effects in the heavy quarkonium radiative electromagnetic decays
• The magnetic dipole transitions in the $(c\bar{b})$ binding system
• Study of the dilepton electromagnetic decays of ${\chi }_{cJ}(1P)$
• Mass spectra, wave functions and mixing effects of the $(bcq)$ baryon