Associated Production of Charmonia-Bottomonia with Color-Octet Channels at the Z Factory, CEPC and FCC-ee

TL;DR

This study analyzes the production of charmonia and bottomonia at future Z factories within the NRQCD framework, highlighting the dominance of color-octet channels and the impact of relativistic corrections on cross sections.

Contribution

It provides the first detailed analysis of charmonia-bottomonia associated production including color-octet channels at future electron-positron colliders, with relativistic corrections quantified.

Findings

Color-octet contributions dominate total cross sections.

Relativistic corrections reduce cross sections by about 50%.

Predicted event numbers are 1-13 at future colliders.

Abstract

Within the nonrelativistic QCD (NRQCD) framework, we investigate the associated production of charmonia+bottomonia at future super $Z$ factory and at the CEPC/FCC-ee. The color-octet(CO) channels in the $\gamma^*/Z^0$-propagated process are considered besides the color-singlet(CS) channels. We find that the contributions of the CO states to the total cross section are dominant for almost all processes from the production threshold to the $Z^0$ mass. Thus, the comparison between the theoretical results and future data may give constraints to the CO matrix elements. In addition, we calculate the relativistic corrections to both the CS and CO channels, which decrease the cross sections significantly, with the $K$ factor $\simeq0.5$. The predicted events of ($J/\psi+\Upsilon$, $\Upsilon+\eta_c$) production, with $J/\psi, \Upsilon$ reconstructed by lepton pair and $\eta_c$ reconstructed by hadronic decays, are (1,1) and (13,10) at the CEPC(2-yr) and FCC-ee(4-yr), respectively.