Relativistic corrections to $J/\psi$ exclusive and inclusive double charm production at B factories

Abstract

In order to clarify the puzzling problems in double charm production, relativistic corrections at order $v^2$ to the processes $e^{+}{e}^{-}\to J/\psi +{\eta }_c$ and $e^{+}{e}^{-}\to J/\psi +c\bar{c}$ at B factories are studied in non-relativistic quantum chromodynamics. The short-distance parts of production cross sections are calculated perturbatively, while the long-distance matrix elements are estimated from $J/\psi$ and ${\eta }_c$ decays up to errors of order $v^4$. Our results show that the relativistic correction to the exclusive process $e^{+}{e}^{-}\to J/\psi +{\eta }_c$ is significant, which, when combined together with the next-to-leading order ${\alpha }_s$ corrections, could resolve the large discrepancy between theory and experiment; whereas for the inclusive process $e^{+}{e}^{-}\to J/\psi +c\bar{c}$ the relativistic correction is tiny and negligible. The physical reason for the above difference between exclusive and inclusive processes largely lies in the fact that in the exclusive process the relative momentum between quarks in charmonium substantially reduces the virtuality of the gluon that converts into a charm quark pair, but this is not the case for the inclusive process, in which the charm quark fragmentation $c\to J/\psi +c$ is significant, and QCD radiative corrections can be more essential.

Version to appear in PRD. In the summary an explicit statement added: "for the J/ψeta_c cross section the relativistic correction alone gives an enhancement factor of 1.7 while the combination of relativistic correction with QCD radiative correction results in a much larger enhancement factor of 9". One reference added. A few typos corrected

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• Resummation of Relativistic Corrections to e+ e- -> J/psi+eta_c
• QCD corrections to double J/ψproduction in e+e- annihilation at \sqrt{s}=10.6 GeV
• Interpretations for the X(4160) observed in the double charm production at B factories
• Exclusive heavy quarkonium + gamma production from e+ e- annihilation into a virtual photon
• Exclusive Double Charmonium Production from ${\rm Y}$ Decay
• The study of leading twist light cone wave functions of 2S state charmonium mesons
• Study of exclusive processes e^+ e^- \to VP
• The color-singlet contribution to e^+ e^- ->J/psi + X at the endpoint
• The study of double vector charmonium mesons production at B-factories within light cone formalism