Heavy quarkonium production through the top quark rare decays via the channels involving flavor changing neutral currents

In the paper, we discuss the possibility of observation of heavy quarkoniums via the processes involving flavor changing neutral currents (FCNC). More explicitly, we systematically calculate the production of heavy charmonium and $(c\bar{b})$-quarkonium through the top quark semi-exclusive rare FCNC decays in the framework of the non-relativistic QCD (NRQCD) factorization theory. Our results show that the total decay widths $\Gamma_{t\to \eta_c} =1.20^{+1.04+1.14}{-0.51-0.45}\times 10^{-16}$GeV,$\Gamma{t\to J/\psi} =1.37^{+1.03+1.30}{-0.51-0.51}\times 10^{-16}$GeV,$\Gamma{t\to B_c}=2.06^{+0.17+0.91}{-0.17-0.54}\times 10^{-18}$GeV,and$\Gamma{t\to B^*c}=6.27^{+0.63+2.78}{-0.62-1.64}\times 10^{-18}$ GeV, where the uncertainties are from variation of quark masses and renormalization scales. Even though the decay widths are small, it is important to make a systematic study on the production of charmonium and $(c\bar{b})$-quarkonium through the top-quark decays via FCNC in the Standard Model, which will provide useful guidance for future new physics research from the heavy quarkonium involved processes.