Heavy quarkonium wave functions at the origin and excited heavy quarkonium production via top quark decays at the LHC

The value of quarkonium wave function at the origin is an important quantity while studying many physical problems concerning a heavy quarkonium. This is because that it is widely used to evaluate the production and decay amplitudes of the heavy quarkonium within the effective filed theory framework, e.g., the non-relativistic QCD (NRQCD). In this paper, the value of the Schr${\rm \ddot{o}}$dinger radial wave function or its first nonvanishing derivative at zero quark-antiquark separation, i.e., $|(|c\bar{c})[n]\rangle$-, $|(|b\bar{c})[n]\rangle$-, and $|(b\bar{b})[n]\rangle$-quarkonium, have been tabulated under five potential models with new parameters of the heavy quarkonium. Moreover, the production of the lower-level Fock states $|(b\bar{Q})[1S]\rangle$ and $|(b\bar{Q})[1P]\rangle$, together with the higher excited Fock states $|(b\bar{Q})[nS]\rangle$ and $|(b\bar{Q})[nP]\rangle$ ($Q$ stands for $c$- or $b$-quark; $n=2,\cdots,6 $) through top quark decays have been studied with the new values of heavy quarkonium wave functions at the origin under the framework of NRQCD. At the LHC with the luminosity ${\cal L}\propto 10^{34}cm^{-2}s^{-1}$ and the center-of-mass energy $\sqrt{S}=14$ TeV, sizable heavy quarkonium events can be produced through top quark decays, i.e., $4 \times10^5$ $B_c$ and $B^*_c$, and $2 \times10^4$ $\eta_b$ and $\Upsilon$ events per year can be obtained according to our calculation.