Revisiting the Heavy Vector Quarkonium Leptonic Widths

Abstract

We revisit the heavy quarkonium leptonic decays $\psi (nS)\to {\ell }^{+}{\ell }^{-}$ and ${\rm Y}(nS)\to {\ell }^{+}{\ell }^{-}$ using the Bethe-Salpeter method. The emphasis is on the relativistic correction. For the $\psi (1S-5S)$ decays, the relativistic effects are $22_{-2}^{+3}\%$, $34_{-5}^{+5}\%$, $41_{-6}^{+6}\%$, $52_{-13}^{+11}\%$ and $62_{-12}^{+14}\%$, respectively. For the ${\rm Y}(1S-5S)$ decays, the relativistic effects are $14_{-2}^{+1}\%$, $23_{-3}^{+0}\%$, $20_{-2}^{+8}\%$, $21_{-7}^{+6}\%$ and $28_{-7}^{+2}\%$, respectively. Thus, the relativistic corrections are large and important in heavy quarkonium leptonic decays, especially for the highly excited charmonium. Our results for ${\rm Y}(nS)\to {\ell }^{+}{\ell }^{-}$ are consistent with the experimental data.

Comments: 22 pages, 3 figures, 6 tables