Heavy Quarkonium Production at LHC through $W$ Boson Decays

Abstract

The production of the heavy $(c\bar{c})$-quarkonium, $(c\bar{b})$-quarkonium and $(b\bar{b})$-quarkonium states ($(Q\overline{Q^{\prime }})$-quarkonium for short), via the $W^{+}$ semi-inclusive decays, has been systematically studied within the framework of the non-relativistic QCD. In addition to the two color-singlet $S$-wave states, we also discuss the production of the four color-singlet $P$-wave states $|(Q\overline{Q^{\prime }}){(}^1{P}_1{)}_1>$ and $(Q\overline{Q^{\prime }}){(}^3{P}_J{)}_1>$ (with $J=(1,2,3)$) together with the two color-octet components $|(Q\overline{Q^{\prime }}){(}^1{S}_0{)}_8>$ and $|(Q\overline{Q^{\prime }}){(}^3{S}_1{)}_8>$. Improved trace technology is adopted to derive the simplified analytic expressions at the amplitude level, which shall be useful for dealing with the following cascade decay channels. At the LHC with the luminosity $\mathcal{L}\propto 10^{34}c{m}^{-2}{s}^{-1}$ and the center-of-mass energy $\sqrt{S}=14$ TeV, sizable heavy-quarkonium events can be produced through the $W^{+}$ boson decays, i.e. $2.57\times 10^6$ ${\eta }_c$, $2.65\times 10^6$ $J/\Psi$ and $2.40\times 10^6$ $P$-wave charmonium events per year can be obtained; and $1.01\times 10^5$ $B_c$, $9.11\times 10^4$ $B_c^{\ast }$ and $3.16\times 10^4$ $P$-wave $(c\bar{b})$-quarkonium events per year can be obtained. Main theoretical uncertainties have also been discussed. By adding the uncertainties caused by the quark masses in quadrature, we obtain ${\Gamma }_{W^{+}\to (c\bar{c})+c\bar{s}}=524.8_{-258.4}^{+396.3}$ KeV, ${\Gamma }_{W^{+}\to (c\bar{b})+b\bar{s}}=13.5_{-3.29}^{+4.73}$ KeV, ${\Gamma }_{W^{+}\to (c\bar{b})+c\bar{c}}=1.74_{-0.73}^{+1.98}$ KeV and ${\Gamma }_{W^{+}\to (b\bar{b})+c\bar{b}}=38.6_{-9.69}^{+13.4}$ eV.

Comments: 24 pages, 12 figures. References updated. To be published in Phys.Rev. D. To match the published version