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Next-to-Leading Order QCD Correction to $\bm{e^+ e^- \to J/ψ+ η_c}$ at $\sqrt {s}=10.6$GeV}

Y. J. Zhang, Y. J. Gao, K. T. Chao

TL;DR

It is found that the NLO QCD correction can substantially enhance the cross section with a K factor (the ratio of NLO to LO) of about 1.8-2.1; hence, it greatly reduces the large discrepancy between theory and experiment.

Abstract

One of the most challenging open problems in heavy quarkonium physics is the double charm production in $e^+e^-$ annihilation at B factories. The measured cross section of $e^+ e^- \to J/ψ+ η_c$ is much larger than leading order (LO) theoretical predictions. With the nonrelativistic QCD factorization formalism, we calculate the next-to-leading order (NLO) QCD correction to this process. Taking all one-loop self-energy, triangle, box, and pentagon diagrams into account, and factoring the Coulomb-singular term into the $c\bar c$ bound state wave function, we get an ultraviolet and infrared finite correction to the cross section of $e^+e^-\to J/ψ+ η_c$ at $\sqrt{s} =10.6$ GeV. We find that the NLO QCD correction can substantially enhance the cross section with a K factor (the ratio of NLO to LO) of about 1.8-2.1; hence it greatly reduces the large discrepancy between theory and experiment. With $m_c=1.4{\rm GeV}$ and $μ=2m_c$, the NLO cross section is estimated to be 18.9 fb, which reaches to the lower bound of experiment.

Next-to-Leading Order QCD Correction to $\bm{e^+ e^- \to J/ψ+ η_c}$ at $\sqrt {s}=10.6$GeV}

TL;DR

It is found that the NLO QCD correction can substantially enhance the cross section with a K factor (the ratio of NLO to LO) of about 1.8-2.1; hence, it greatly reduces the large discrepancy between theory and experiment.

Abstract

One of the most challenging open problems in heavy quarkonium physics is the double charm production in annihilation at B factories. The measured cross section of is much larger than leading order (LO) theoretical predictions. With the nonrelativistic QCD factorization formalism, we calculate the next-to-leading order (NLO) QCD correction to this process. Taking all one-loop self-energy, triangle, box, and pentagon diagrams into account, and factoring the Coulomb-singular term into the bound state wave function, we get an ultraviolet and infrared finite correction to the cross section of at GeV. We find that the NLO QCD correction can substantially enhance the cross section with a K factor (the ratio of NLO to LO) of about 1.8-2.1; hence it greatly reduces the large discrepancy between theory and experiment. With and , the NLO cross section is estimated to be 18.9 fb, which reaches to the lower bound of experiment.

Paper Structure

This paper contains 12 equations, 3 figures.

Figures (3)

  • Figure 1: Born diagrams for $e^-(k_1) e^+ (k_2)\to J/\psi(2p_1) \eta_c(2p_2)$.
  • Figure 2: Twelve of the twenty-four box and pentagon diagrams for $e^-(k_1) e^+ (k_2)\to J/\psi(2p_1) \eta_c(2p_2)$.
  • Figure 3: Cross sections as functions of the renormalization scale $\mu$. Here $|R_S(0)|^2=0.978 {\rm GeV}^3$, $\Lambda=0.338 {\rm GeV}$, $\sqrt s=10.6{\rm GeV}$; NLO results are represented by solid lines and LO one by dashed lines; the upper line is for $m=1.4{\rm GeV}$ and the corresponding lower line is for $m=1.5{\rm GeV}$; the upper straight line denotes the central value measured by Belle in Eq.(\ref{['Belle']}) and the lower straight line by BaBar in Eq.(\ref{['BaBar']}).