Revisiting the <i>S</i> -wave leptonic decay widths of charmonium and bottomonium via single-photon annihilation using the Bethe–Salpeter approach

We revisit the leptonic decay widths of S-wave vector quarkonia, specifically the charmonium ([Formula: see text]) and bottomonium ([Formula: see text]) families, through the single-photon annihilation process into lepton pairs. The analysis is conducted within the relativistic Bethe–Salpeter framework using an instantaneous kernel and a unified parameter set applied consistently across both charm and bottom sectors. This approach allows for a comprehensive calculation of mass spectra and leptonic widths for the [Formula: see text]–[Formula: see text] states, as well as the ratios of excited-state widths to ground-state widths. Our results show strong agreement with experimental data for the ground and first excited states. The moderate deviations observed in higher radial excitations are attributed to nodal structure sensitivities and omitted higher-order radiative and relativistic corrections. Unlike standard nonrelativistic QCD (NRQCD) studies, this Bethe–Salpeter treatment offers a more rigorous relativistic handling of the bound-state dynamics. Furthermore, the use of a unified parametrization is supported by recent heavy-flavor scaling regularities in heavy baryons, providing a systematically improvable description of electromagnetic decays in heavy quarkonia.