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Search for excited charmonium states in $e^+e^-$ Annihilation at $\sqrt{s}=10.6$ GeV

Kui-Yong Liu, Zhi-Guo He, Kuang-Ta Chao

TL;DR

The study applies leading-order NRQCD, including both QCD and QED contributions, to predict cross sections for a wide array of double-charmonium final states in $e^+e^-$ annihilation at $\sqrt{s}=10.6$ GeV. By detailing the formalism, wavefunction inputs, and channel-specific results across $S$-, $P$-, and $D$-wave combinations, it identifies promising modes for observing excited charmonia such as $\eta_c(3S)$, $\chi_{c0}(2P)$, and $h_c$, and discusses implications for Belle/Babar results and potential X states. The work highlights that relative production rates can be informative about the production mechanism and spectroscopy, though absolute rates require higher-order and nonperturbative corrections. It also shows that QED contributions, while generally modest, can affect specific channels and should be included in precise predictions. Overall, double-charmonium production at B factories is presented as a valuable probe of charmonium spectroscopy and QCD dynamics.

Abstract

We suggest searching for excited charmonium states in $e^+e^-$ annihilation via double charmonium production at $\sqrt{s}=10.6$ GeV with $B$ factories, based on a more complete leading order calculation including both QCD and QED contributions for various processes. In particular, for the C=+ states, the $χ_{c0}(nP)$ (n=2,3) and $η_c(mS)$ (m=3,4) may have appreciable potentials to be observed; while for the C=- states, the $η_ch_c$ production and especially the $χ_{c1}h_c$ production might provide opportunities for observing the $h_c$ with higher statistics in the future. A brief discussion for the X(3940) observed in the double charmonium production is included.

Search for excited charmonium states in $e^+e^-$ Annihilation at $\sqrt{s}=10.6$ GeV

TL;DR

The study applies leading-order NRQCD, including both QCD and QED contributions, to predict cross sections for a wide array of double-charmonium final states in annihilation at GeV. By detailing the formalism, wavefunction inputs, and channel-specific results across -, -, and -wave combinations, it identifies promising modes for observing excited charmonia such as , , and , and discusses implications for Belle/Babar results and potential X states. The work highlights that relative production rates can be informative about the production mechanism and spectroscopy, though absolute rates require higher-order and nonperturbative corrections. It also shows that QED contributions, while generally modest, can affect specific channels and should be included in precise predictions. Overall, double-charmonium production at B factories is presented as a valuable probe of charmonium spectroscopy and QCD dynamics.

Abstract

We suggest searching for excited charmonium states in annihilation via double charmonium production at GeV with factories, based on a more complete leading order calculation including both QCD and QED contributions for various processes. In particular, for the C=+ states, the (n=2,3) and (m=3,4) may have appreciable potentials to be observed; while for the C=- states, the production and especially the production might provide opportunities for observing the with higher statistics in the future. A brief discussion for the X(3940) observed in the double charmonium production is included.

Paper Structure

This paper contains 15 sections, 64 equations, 8 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Formulas and calculations
  3. The $\psi(nS)\eta_c(mS)$ production
  4. The $\psi(nS)\chi_{cJ}(mP) (J=0,1,2)$ production
  5. The $\eta_c(nS) h_c(mP)$ production
  6. The $\chi_{cJ}(nP)(J=0,1,2)h_c(mP)$ production
  7. The $\psi(nS)^1D_2(mP)$ production
  8. The $\chi_{cJ}(nP)(J=0,1,2)^3D_J'(mD)(J'=1,2,3)$ production
  9. QED processes including $J^{PC}=1^{--}$ states
  10. The $\psi(nS)\eta_c(mS)$ production
  11. The $\psi(ns)+\chi_{cJ}(mp)$ Production
  12. The $\psi(ns)+1D2$ Production
  13. The $\eta_c(ns)+\psi_{3D1}$ Production
  14. conclusion
  15. Discussion and Summary

Figures (8)

  • Figure 1: Differential cross sections for $e^+e^- \rightarrow J/\psi+\chi_{cJ}(\eta_c)$
  • Figure 2: Differential cross sections for $e^+e^- \rightarrow \eta_c+ h_c$
  • Figure 3: Differential cross sections for $e^+e^- \rightarrow \chi_{c1}+h_c$
  • Figure 4: Differential cross sections for $e^+e^- \rightarrow \chi_{c2}+ h_c$
  • Figure 5: Differential cross sections for $e^+e^- \rightarrow J/\psi+^1D_2$
  • ...and 3 more figures