Spectroscopy of ground and excited states of pseudoscalar and vector charmonium and bottomonium

Abstract

In this work we calculate the mass spectrum, weak decay constants, two photon decay widths, and two gluon decay widths of ground (1S), and radially excited (2S, 3S,...) states of pseudoscalar charmoniuum and bottomonium such as η c and η b , as well as the mass spectrum and leptonic decay constants of ground state (1S), excited (2S, 1D, 3S, 2D, 4S,...,5D) states of vector charmonium and bottomonium such as J/ψ, and Υ, 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 4 × 4 representation for two-body (qq) 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 eigen functions for ground and excited states so obtained are used to evaluate the decay constants and decay widths for different processes.

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

“…However, the price one pays in this approach is to solve a coupled set of Salpeter equations for both pseudoscalar and vector quarkonia. However, in [21], we explicitly showed that these coupled Salpeter equations can indeed get decoupled in the heavy-quark approximation, leading to mass spectral equations with analytical solutions for both masses, as well as eigenfunctions for all the ground and excited states of pseudoscalar and vector and systems 2 Advances in High Energy Physics in an approximate harmonic oscillator basis. These analytical forms of eigenfunctions for ground and excited states so obtained were used to evaluate the transition amplitudes for different processes in [21].…”

“…However, in [21], we explicitly showed that these coupled Salpeter equations can indeed get decoupled in the heavy-quark approximation, leading to mass spectral equations with analytical solutions for both masses, as well as eigenfunctions for all the ground and excited states of pseudoscalar and vector and systems 2 Advances in High Energy Physics in an approximate harmonic oscillator basis. These analytical forms of eigenfunctions for ground and excited states so obtained were used to evaluate the transition amplitudes for different processes in [21]. Thus, in [21], we had calculated the mass spectrum, weak decay constants, two-photon decay widths and two-gluon decay widths of ground (1 ) and radially excited (2 , 3 , .…”

“…In a recent work [20,21], we employed a 4 × 4 representation for two-body ( ) BS amplitude for calculating both the mass spectra and the transition amplitudes for various processes. However, the price one pays in this approach is to solve a coupled set of Salpeter equations for both pseudoscalar and vector quarkonia.…”

“…These analytical forms of eigenfunctions for ground and excited states so obtained were used to evaluate the transition amplitudes for different processes in [21]. Thus, in [21], we had calculated the mass spectrum, weak decay constants, two-photon decay widths and two-gluon decay widths of ground (1 ) and radially excited (2 , 3 , . .…”

“…However in [22,23], they demonstrated an explicit mathematical procedure for handling such problems in 4 × 4 representation of BSE. Thus, in the present work, we will precisely apply an instantaneous formalism employing 4 × 4 BSE under CIA for transitions involving the process, → , where such problems do not enter in the calculations of [21]. This paper is organized as follows.…”