Abstract We investigate the electromagnetic and hadronic annihilation decay widths of S -wave vector quarkonia, namely charmonium (J/ (nS) J / ψ (n S) ) and bottomonium ( (nS) Υ (n S) ) with radial excitations n=1 n = 1 –4, within the framework of the instantaneous Bethe–Salpeter (BS) equation. The interaction kernel combines a harmonic confinement potential with one-gluon exchange, using a single unified parameter set for both cc c c ¯ and bb b b ¯ systems. The obtained relativistic wave functions are used to compute the decay widths for the processes of nJ/ 3 n J / ψ → 3 γ, nJ/ 3g n J / ψ → 3 g, n 3 n Υ → 3 γ, and n 3g n Υ → 3 g. For the ground state, ₉/ (₁ₒ) ₃ =1. 004 10^-3\, keV Γ J / ψ (1 S) → 3 γ = 1. 004 × 10 - 3 keV agrees well with experiment, while ₉/ (₁ₒ) ₃₆=59. 28\, keV Γ J / ψ (1 <mml
Negash et al. (Wed,) studied this question.