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In this work we study the radiative decay widths of vector quarkonia for theprocess of $J/\psi(nS)\rightarrow\eta_{c}(nS)\gamma$ and$\Upsilon(nS)\rightarrow\eta_{b}(nS)\gamma$ (for principal quantum numbers$n=1, 2, 3$) in the framework of Bethe-Salpeter equation under the covariantinstantaneous ansatz using a $4\times 4$ form of BSE. The parameters of theframework were determined by a fit to the mass spectrum of ground states ofpseudoscalar and vector quarkonia, such as; $\eta_{c}$, $\eta_{b}$, $J/\psi$and $\Upsilon$. These input parameters so fixed were found to give goodagreements with data on mass spectra of ground and excited states ofpseudoscalar and vector quarkonia, leptonic decay constants of pseudoscalar andvector quarkonia, two photon decays and two gluon decays of pseudoscalarquarkonia in our recent paper. With these input parameters so fixed, theradiative decay widths of ground (1S) and excited (2S, 3S) states of heavyvector quarkonia ($J/\Psi$ and $\Upsilon$) are calculated and found to be inreasonable agreement with data.

Radiative decay widths of ground and excited states of vector charmonium and bottomonium