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 ${\eta }_c$ and ${\eta }_b$, as well as the mass spectrum and leptonic decay constants of ground state (1S), excited (2S,1D,3S,2D,4S,and 3D) states of vector charmonium and bottomonium such as $J/\psi$, and ${\rm Y}$, 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 $4\times 4$ representation for two-body ($q\overline{q}$) 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. Further, in the present framework of BSE, the hadron-quark vertex function (and the full 4D BS wave function) for pseudoscalar and vector quarkonia used for calculation of various processes, accommodates all the Dirac structures from their complete set in a natural manner.

33 pages, 5 figure, 6 tables

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• $Q\bar{Q}$ ($Q\in \{b,c\}$) spectroscopy using Cornell potential
• Treating $Z_c(3900)$ and $Z(4430)$ as the ground-state and first radially excited tetraquarks
• Spectroscopy and Decay properties of the charmonium
• Self-consistency and covariance of light-front quark models: testing via $P$, $V$ and $A$ meson decay constants, and $P\to P$ weak transition form factors
• Spectroscopy of all charm tetraquark states
• Analytic approach to calculations of mass spectra and decay constants of heavy-light quarkonia in the framework of Bethe-Salpeter equation
• An approach to calculation of mass spectra and two-photon decays of $c\overline{c}$ mesons in the framework of Bethe-Salpeter Equation
• Revisiting the radiative decays $J/\psi \to \gamma {\eta }^{(\prime )}$ in perturbative QCD
• Revisiting the $P$-wave charmonium radiative decays $h_c\to \gamma {\eta }^{(\prime )}$ with relativistic corrections
• Mass spectra and decay constants of heavy-light axial quarkonia in the framework of Bethe-Salpeter equation
• Radiative decays of heavy-light quarkonia through $M1$, and $E1$ transitions in the framework of Bethe-Salpeter equation
• $E1$ and M1 radiative transitions involving heavy-light axial, pseudoscalar and vector quarkonia in the framework of Bethe-Salpeter equation
• Double charmonium productions in electron-positron annihilation using Bethe-Salpeter approach
• The Radial Excited Heavy Mesons
• Analytical calculations of ground and excited states of unequal mass heavy pseudoscalar and vector mesons mass spectra using Bethe-Salpeter formalism
• Radiative decay widths of ground and excited states of vector charmonium and bottomonium
• QCD analysis of the $P$-wave charmonium electromagnetic Dalitz decays $h_c\to {\eta }^{(\prime )}{\ell }^{+}{\ell }^{-}$
• Heavy quarkonium decay $V\to ggg$ with both relativistic and QCD radiative corrections
• Prospects for observing the ${\eta }_t$ $\to$ $W^{+}{W}^{-}$ decay at the HL-LHC