Heavy quarkonium production through the semi-exclusivee+e−annihilation channels round theZ0peak

Abstract

Within the framework of the nonrelativistic quantum chromodynamics, we present a detailed discussion on the heavy quarkonium production at the leading order in ${\ensuremath{\alpha}}_{s}$ at a ${e}^{+}{e}^{\ensuremath{-}}$ collider with the collision energy around the ${Z}^{0}$ peak. Quarkonia are produced through the semi-exclusive channels ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}|{H}_{Q\overline{Q}}⟩+X$ with $X=Q\overline{Q}$ or $gg$, where $Q$ indicates a heavy quark (respectively, $b$ or $c$). It is noted that in addition to the color-singlet $1S$-level quarkonium states, the $2S$ and $1P$ color-singlet states and the color-octet $|(Q\overline{Q})[1^{3}S_{1}^{(\mathbf{8})}]g⟩$ state also provide sizable contributions. The heavy quarkonium transverse momentum and rapidity distributions for the ${e}^{+}{e}^{\ensuremath{-}}$ collision energy ${E}_{\mathrm{cm}}={m}_{Z}$ are presented. For both charmonium and bottomonium production via the ${Z}^{0}$ propagator, there is approximate ``spin degeneracy'' between the spin-triplet and spin-singlet quarkonium states. Uncertainties for the total cross sections are estimated by taking ${m}_{c}=1.50\ifmmode\pm\else\textpm\fi{}0.15\text{ }\text{ }\mathrm{GeV}$ and ${m}_{b}=4.90\ifmmode\pm\else\textpm\fi{}0.15\text{ }\text{ }\mathrm{GeV}$. Around ${E}_{\mathrm{cm}}={m}_{Z}$, due to the ${Z}^{0}$-boson resonance effect, total cross sections for the channels via the ${Z}^{0}$-propagator become much larger than the channels via the virtual photon propagator. We conclude that, in addition to the $B$ factories such as BABAR and Belle, and the hadronic colliders such as Tevatron and LHC, such a super $Z$ factory will present an excellent platform for studying the heavy quarkonium properties.