Production of double heavy quarkonium at super $Z$ factory

Abstract

Within the color singlet model, we calculate the exclusive production of double charmonia, double bottomonia, and double $B_c$ mesons at future super $Z$ factory. The two heavy quarkonia or $B_c$'s are either two S-wave Fock states (${}^1{S}_0,{}^3{S}_1$), or one S-wave and one P-wave states (${}^1{P}_1,{}^3{P}_J(J=0,1,2)$). The top three $Z^0$ propagated channels in cross sections for double charmonia are $J/\psi +h_c,{\eta }_c+{\chi }_{c2}$, and ${\eta }_c+{\chi }_{c0}$. For double bottomonia, they are ${\eta }_b+{\rm Y},{\rm Y}+{\chi }_{b2}$, and ${\rm Y}+{\rm Y}$. For double $B_c$ mesons, they are $B_c^{\ast +}+B_c^{\ast -}$,$B_c^{\ast +}+{\chi }_{bc2}^{-}$, and ${\eta }_{bc}^{+}+B_c^{\ast -}$. The cross sections of double $B_c$ mesons are roughly one order of magnitude larger than those of the double bottomonia, and two orders of magnitude larger than those of the double charmonia. To make it helpful for experimental study, we present the total cross sections $\sigma$ as functions of CM energy $\sqrt{s}$, $\sigma$ as functions of the renormalization scale $\mu$, the angle distributions $d\sigma /dcos\theta$, and the $p_T$ distributions $d\sigma /d{p}_t$. The uncertainties come from the varying masses of constituent heavy quarks bring up to 20% corrections. We also find that the initial state radiation can bring about 30%$\sim$40% suppresions when 1\%$m_Z$ energy is losing, and cross sections can increase by about $2\sim 3$ times or decrease by an order of magnitude when adopting different potential models which becomes the major source of uncertainty. The numerical results show that it might be not optimistic for the experimental observation, but it is still far from excluded at the FCC-ee and also the CEPC running in the $Z$ factory mode.

15 pages, 6 tables, and 4 figures. Version published at EPJC

References in corpus (16)

• Heavy quarkonium: progress, puzzles, and opportunities
• QCD corrections to J/psi plus eta_c production in e+e- annihilation at sqrt{s}=10.6 GeV
• Resummation of Relativistic Corrections to e+ e- -> J/psi+eta_c
• Pair Production of Heavy Quarkonium and $B_c{(}^{\ast })$ Mesons at Hadron Colliders
• Production of $B_c$ or ${\bar{B}}_c$ meson and its excited states via $\bar{t}$-quark or $t$-quark decays
• $Z_0$ Boson Decays to $B_c^{(\ast )}$ Meson and Its Uncertainties
• Complete NLO QCD study of single- and double-quarkonium hadroproduction in the colour-evaporation model at the Tevatron and the LHC
• Next-to-leading order QCD corrections to paired $B_c$ production in $e^{+}{e}^{-}$ annihilation
• Excited Heavy Quarkonium Production at the LHC through $W$-Boson Decays
• Heavy quarkonium wave functions at the origin and excited heavy quarkonium production via top quark decays at the LHC
• NLO QCD corrections to $B_c$-pair production in photon-photon collision
• Associated charmonium-bottomonium production in a single boson $e^{+}{e}^{-}$ annihilation
• Photoproduction of the double $J/\psi$ (${\rm Y}$) at the LHC with forward proton tagging
• A short theoretical review of charmonium production
• Next-to-leading-order QCD correction to the exclusive double charmonium production via $Z$ decays
• Soft Gluon Resummation in Double Heavy Quarkonium Production at LHC

Cited by in corpus (1)

• Rare and exclusive few-body decays of the Higgs, Z, W bosons, and the top quark