Weak decays of J/\psi and {\rm{\Upsilon }}(1S)

In this paper we study the weak decays of J/\psi and {{\Upsilon }}(1S). The cases when the final mesons are pseudo-scalars or vectors are considered. Using the Bethe-Salpeter method, we calculate the hadronic transition amplitude and give the form factors. The energy spectra of leptons for the semi-leptonic channels are also presented for convenience. In the calculation of non-leptonic decays, the naive factorization is applied. And all types of such channels, namely, flavor-favored or suppressed and color-favored or suppressed, are calculated. Our results show that, for the semi-leptonic decay modes, the largest branching ratios are of the order of 10^-10 both for J/\psi and {{\Upsilon }}(1S) decays, and the largest branching ratios of non-leptonic decays are of the order of 10^-9 for J/\psi and 10^-10 for {{\Upsilon }}(1S).