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Exclusive Double-Charmonium Production from e^+ e^- Annihilation into a Virtual Photon

Eric Braaten, Jungil Lee

TL;DR

This work applies NRQCD-inspired color-singlet calculations to exclusive double-charmonium production in e+e- annihilation via a virtual photon, revealing sizable purely electromagnetic contributions that can significantly alter predicted cross sections. It provides comprehensive analytic expressions across S-, P-, and D-wave combinations, incorporates relativistic corrections through NRQCD velocity expansions, and derives NRQCD matrix elements from potential models and experimental widths. The study yields predictions for B-factory energies, discusses perturbative and color-octet uncertainties, and identifies promising channels such as J/ψ+η_{c2}(1D) and ψ_2(1D) that could be observable, while also confronting BELLE’s J/ψ+η_c measurement with substantial theoretical uncertainties. Overall, the results offer a stringent testbed for NRQCD factorization and relativistic effects in exclusive quarkonium production.

Abstract

We calculate the exclusive cross sections for e^+ e^- annihilation into two charmonium states through a virtual photon. Purely electromagnetic contributions are surprisingly large, changing the cross sections by as much as 21%. The predicted cross section for J/psi + eta_c is about an order of magnitude smaller than a recent measurement by the BELLE Collaboration, although part of the discrepancy can be attributed to large relativistic corrections. The cross sections for S-wave + P-wave, P-wave + P-wave, and S-wave + D-wave charmonium states are also calculated. It may be possible to discover the D-wave state eta_{c2}(1D) at the B factories through the mode J/psi+η_{c2}, whose cross section is predicted to be about a factor of 10 smaller than J/psi + eta_c.

Exclusive Double-Charmonium Production from e^+ e^- Annihilation into a Virtual Photon

TL;DR

This work applies NRQCD-inspired color-singlet calculations to exclusive double-charmonium production in e+e- annihilation via a virtual photon, revealing sizable purely electromagnetic contributions that can significantly alter predicted cross sections. It provides comprehensive analytic expressions across S-, P-, and D-wave combinations, incorporates relativistic corrections through NRQCD velocity expansions, and derives NRQCD matrix elements from potential models and experimental widths. The study yields predictions for B-factory energies, discusses perturbative and color-octet uncertainties, and identifies promising channels such as J/ψ+η_{c2}(1D) and ψ_2(1D) that could be observable, while also confronting BELLE’s J/ψ+η_c measurement with substantial theoretical uncertainties. Overall, the results offer a stringent testbed for NRQCD factorization and relativistic effects in exclusive quarkonium production.

Abstract

We calculate the exclusive cross sections for e^+ e^- annihilation into two charmonium states through a virtual photon. Purely electromagnetic contributions are surprisingly large, changing the cross sections by as much as 21%. The predicted cross section for J/psi + eta_c is about an order of magnitude smaller than a recent measurement by the BELLE Collaboration, although part of the discrepancy can be attributed to large relativistic corrections. The cross sections for S-wave + P-wave, P-wave + P-wave, and S-wave + D-wave charmonium states are also calculated. It may be possible to discover the D-wave state eta_{c2}(1D) at the B factories through the mode J/psi+η_{c2}, whose cross section is predicted to be about a factor of 10 smaller than J/psi + eta_c.

Paper Structure

This paper contains 24 sections, 57 equations, 2 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Color-Singlet Model Calculations
  3. Asymptotic behavior
  4. Projections onto charmonium states
  5. $\bm{S}$-wave + $\bm{S}$-wave
  6. $\bm{S}$-wave + $\bm{P}$-wave
  7. $\bm{P}$-wave + $\bm{P}$-wave
  8. $\bm{S}$-wave + $\bm{D}$-wave
  9. NRQCD matrix elements
  10. Potential models
  11. Phenomenology
  12. Relativistic corrections
  13. NRQCD factor
  14. Relativistic correction factor
  15. Predictions for $\bm{B}$ factories
  16. ...and 9 more sections

Figures (2)

  • Figure 1: QCD diagrams that can contribute to the color-singlet process $\gamma^* \to c \bar{c}_1 + c \bar{c}_1$.
  • Figure 2: QED diagrams that contribute to the color-singlet process $\gamma^* \to c \bar{c}_1(^3S_1) + c \bar{c}_1$.