  The top quark decay process $\tcups$ is studied in the Standard Model and the
Minimal Supersymmetric Standard Model with conserved and violated $R-$parity.
In dealing with the heavy quarkonium, $\ups$, production, we take both
color-singlet and -octet mechanisms into consideration. With numerical analysis
it is found that within the Standard Model the decay rate of the concerned
process is beyond the border of reachable level of the next round of
experiment, though it is much larger than that of the rare top decays, while
extra new contributions from beyond the Standard Model could enhance the decay
rate by several orders. It is also noticed that a precise measurement of the
charged Higgs mass without $\tan\beta$ dependence is possible via this process.

High Energy Physics - Phenomenology