Spectroscopy of ground and excited states of pseudoscalar and vector charmonium and bottomonium
Abstract
In this paper, we calculate the mass spectrum, weak decay constants, two photon decay widths, and two-gluon decay widths of ground () and radially excited () states of pseudoscalar charmoniuum and bottomonium such as and , as well as the mass spectrum and leptonic decay constants of ground state (), excited () states of vector charmonium and bottomonium such as , and , using the formulation of Bethe–Salpeter equation under covariant instantaneous ansatz (CIA). Our results are in good agreement with data (where ever available) and other models. In this framework, from the beginning, we employ a representation for two-body () BS amplitude for calculating both the mass spectra as well as the transition amplitudes. However, the price we have to pay is to solve a coupled set of equations for both pseudoscalar and vector quarkonia, which we have explicitly shown get decoupled in the heavy-quark approximation, leading to mass spectral equation with analytical solutions for both masses, as well as eigenfunctions for all the above states, in an approximate harmonic oscillator basis. The analytical forms of eigenfunctions for ground and excited states so obtained are used to evaluate the decay constants and decay widths for different processes.
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