2010/03/19 by C. C. Chang, Chao-Hsi Chang, Guo‐Li Wang +1 · 2 citations
Physics and Astronomy · #High-Energy Particle Collisions Research #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions #hep-ph
paper · pdf · doi:10.1007/s11433-010-4156-1
published as Sci. China G53:2005-2018,2010 · 26 pages, 8 figures
arxiv created 2010/03/19 · openalex publication_date 2010/10/26 · arxiv updated 2011/01/28 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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 JPC=1-- states, P-F wave mixing in JPC=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).