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Resummation of Relativistic Corrections to e+ e- -> J/psi+eta_c

Geoffrey T. Bodwin, Jungil Lee, Chaehyun Yu

TL;DR

This work delivers a refined NRQCD-based calculation of relativistic corrections to e+e- → J/ψ + η_c at B-factory energies, incorporating resummation of a class of v-expansion terms, VMD treatment for photon fragmentation, running α effects, and the interference with NLO α_s corrections. Using improved NRQCD matrix elements with a detailed correlated-uncertainty analysis, the authors obtain a central cross section of about 17.6 fb at √s = 10.58 GeV, with sizable but well-characterized uncertainties that account for both perturbative and nonperturbative sources. The direct relativistic corrections rise the cross section by roughly 40%, while NLO α_s effects and their interference contribute substantially, and the VMD refinement modestly shifts the central value. The results align with Belle and BABAR within uncertainties, effectively resolving the long-standing discrepancy and highlighting remaining theoretical uncertainties dominated by uncalculated α_s v^2 and α_s^2 terms and NRQCD-factorization assumptions.

Abstract

We present a new calculation, in the nonrelativistic QCD (NRQCD) factorization formalism, of the relativistic corrections to the double-charmonium cross section sigma[e+ e- -> J/psi+eta_c] at the energy of the Belle and BABAR experiments. In comparison with previous work, our calculation contains several refinements. These include the use of the improved results for the nonperturbative NRQCD matrix elements, the resummation of a class of relativistic corrections, the use of the vector-meson-dominance method to calculate the fragmentation contribution to the pure QED amplitude, the inclusion of the effects of the running of alpha, and the inclusion of the contribution that arises from the interference between the relativistic corrections and the corrections of next-to-leading order in alpha_s. We also present a detailed estimate of the theoretical uncertainty. We conclude that the discrepancy between the theoretical prediction for sigma[e+e- -> J/psi+eta_c] and the experimental measurements has been resolved.

Resummation of Relativistic Corrections to e+ e- -> J/psi+eta_c

TL;DR

This work delivers a refined NRQCD-based calculation of relativistic corrections to e+e- → J/ψ + η_c at B-factory energies, incorporating resummation of a class of v-expansion terms, VMD treatment for photon fragmentation, running α effects, and the interference with NLO α_s corrections. Using improved NRQCD matrix elements with a detailed correlated-uncertainty analysis, the authors obtain a central cross section of about 17.6 fb at √s = 10.58 GeV, with sizable but well-characterized uncertainties that account for both perturbative and nonperturbative sources. The direct relativistic corrections rise the cross section by roughly 40%, while NLO α_s effects and their interference contribute substantially, and the VMD refinement modestly shifts the central value. The results align with Belle and BABAR within uncertainties, effectively resolving the long-standing discrepancy and highlighting remaining theoretical uncertainties dominated by uncalculated α_s v^2 and α_s^2 terms and NRQCD-factorization assumptions.

Abstract

We present a new calculation, in the nonrelativistic QCD (NRQCD) factorization formalism, of the relativistic corrections to the double-charmonium cross section sigma[e+ e- -> J/psi+eta_c] at the energy of the Belle and BABAR experiments. In comparison with previous work, our calculation contains several refinements. These include the use of the improved results for the nonperturbative NRQCD matrix elements, the resummation of a class of relativistic corrections, the use of the vector-meson-dominance method to calculate the fragmentation contribution to the pure QED amplitude, the inclusion of the effects of the running of alpha, and the inclusion of the contribution that arises from the interference between the relativistic corrections and the corrections of next-to-leading order in alpha_s. We also present a detailed estimate of the theoretical uncertainty. We conclude that the discrepancy between the theoretical prediction for sigma[e+e- -> J/psi+eta_c] and the experimental measurements has been resolved.

Paper Structure

This paper contains 16 sections, 52 equations, 2 figures, 2 tables.

Table of Contents

  1. Introduction
  2. General Form of the amplitude for $\bm{e^+e^-\to J/\psi+\eta_c}$
  3. Amplitude for $\bm{\gamma^\ast\to} \bm{Q}\bar{\bm{Q}} \bm{({}^3S_1)} \bm{+} \bm{Q}\bar{\bm{Q}}\bm{({}^1S_0)}$
  4. Kinematics
  5. Spin and color projectors
  6. Projections of the four-quark states
  7. NRQCD expansion of the amplitude and matching
  8. Resummation
  9. Choice of frame and co-ordinate system
  10. Cross section
  11. VMD treatment of the photon-fragmentation amplitude
  12. Choice of the quarkonium masses
  13. Interference with the NLO amplitude
  14. Results
  15. Comparison with previous calculations
  16. ...and 1 more sections

Figures (2)

  • Figure 1: Feynman diagrams for the process $e^+ e^- \to J/\psi + \eta_c$ at leading order in $\alpha_s$. The wavy line represents a photon, the curly line represents a gluon, and the straight lines represent the leptons and heavy quarks. There are six additional diagrams that can be obtained by reversing the directions of the arrows on the heavy-quark lines and/or by replacing the gluon by a photon.
  • Figure 2: Feynman diagram for the process $e^+ e^- \to J/\psi + \eta_c$ in which a photon fragments into a $J/\psi$. There is an additional diagram that can be obtained by reversing the directions of the arrows on the heavy-quark line on the $\eta_c$ side.