${\bar{B}^{0}_{s}}$ and its excited meson production via top quark decays at the LHC

TL;DR

This paper calculates the masses and wave functions of $B_s$ mesons using potential models, then studies their production via top quark decays at the LHC, providing analytical decay results and estimating event yields.

Contribution

It offers a systematic analysis of $B_s$ meson production from top decays, including new potential model calculations and the application of improved trace technology for decay amplitude analysis.

Findings

Masses and wave functions of $B_s$ mesons calculated under various potential models.

Estimated decay width of top quark to $B_s$ mesons and W boson with uncertainties.

Approximately 1.3 million $B_s$ meson events produced annually at the LHC from top decays.

Abstract

In this work we evaluate the masses of the $|(b\bar{s})[n]\rangle$ or $|(\bar{b}s)[n]\rangle$ quarkonium ($\bar{B}^{0}_{s}$ or ${B}^{0}_{s}$ meson) under the B.T. potential, and the values of the Schr${\rm \ddot{o}}$dinger radial wave function at the origin of the $|(b\bar{s})[n]\rangle$ or $|(\bar{b}s)[n]\rangle$ quarkonium within the five potential models. Then we investigate a systematic study on the production of the $|(b\bar{s})[n]\rangle$ or $|(\bar{b}s)[n]\rangle$ quarkonium via top quark or antitop quark decays in the color-singlet QCD factorization formula (CSQCDFF), i.e., the two $S$-wave states, $|(b\bar{s})[1^1S_0] \rangle$ (or $|(\bar{b}s)[1^1S_0] \rangle$) and $|(b\bar{s})[1^3S_1] \rangle$ (or $|(\bar{b}s)[1^3S_1] \rangle$), and its four $P$-wave excited states, $|(b\bar{s})[1^1P_1] \rangle$ (or $|(\bar{b}s)[1^1P_1] \rangle$) and $|(b\bar{s})[1^3P_J] \rangle$ (or $|(\bar{b}s)[1^3P_J] \rangle$) (with $J =[0, 1, 2]$). For deriving compact analytical results for complex processes, the "improved trace technology" is adopted to deal with the decay channels at the amplitudes. Moreover, various differential distributions and uncertainties of the concerned processes are analyzed carefully. By adding the uncertainties caused by the ${b}$ and ${s}$-quark masses in quadrature, we obtain $\Gamma{(t\to |(b\bar{s})[n]\rangle +W^{+}s)}=14.19^{+4.36}_{-3.20}$~MeV. 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 $|(b\bar{s})[n]\rangle$ or $|(\bar{b}s)[n]\rangle$ meson events can be produced through ${t}$-quark or ${\bar{t}}$-quark decays; i.e., about $1.3~\times10^6$ ${\bar{B}^0_s}$ or ${B^0_s}$ events per year can be obtained.