Study of $e^+ e^- \to \pi^+ \pi^- J/\psi$ and Observation of a Charged Charmonium-like State at Belle

E. A. Kuraev and V. S. Fadin, Sov. J. Nucl. Phys. 41

1985

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In the paper, M ⁡ ( π + ​ π − ​ ℓ + ​ ℓ − ) − M ⁡ ( ℓ + ​ ℓ − ) + M ⁡ ( J / ψ ) M(\pi^{+}\pi^{-}\ell^{+}\ell^{-})-M(\ell^{+}\ell^{-})+M(J/\psi) is used instead of the invariant mass of the four final state particles to improve the mass resolution. Here M ⁡ ( J / ψ ) M(J/\psi) is the nominal mass of the J / ψ J/\psi

Cited in the paper.

The cross sections are measured to be ( 13.79 ± 0.44 ± 0.83 ) (13.79\pm 0.44\pm 0.83) pb and ( 13.33 ± 0.25 ± 0.70 ) (13.33\pm 0.25\pm 0.70) pb at s = 10.87 \sqrt{s}=10.87 GeV, ( 16.75 ± 0.85 ± 1.01 ) (16.75\pm 0.85\pm 1.01) pb and ( 16.63 ± 0.54 ± 0.87 ) (16.63\pm 0.54\pm 0.87) pb at s = 10.02 \sqrt{s}=10.02 GeV, for the e + ​ e − e^{+}e^{-} and μ + ​ μ − \mu^{+}\mu^{-} modes, respectively. Our measurements agree with the predictions of ( 13.42 ± 0.25 ) (13.42\pm 0.25) pb at 10.87 GeV, and ( 16.03 ± 0.29 ) (16.03\pm 0.29) pb at 10.02 GeV [ 18 ] within errors

Cited in the paper.

Considering the correlation between Γ e ​ e ​ ℬ ​ ( R → π + ​ π − ​ J / ψ ) \Gamma_{ee}\mathcal{B}(R\to\pi^{+}\pi^{-}J/\psi) and Γ tot \Gamma_{{\textrm{tot}}} , we get ℬ e ​ e ​ ℬ ​ ( R → π + ​ π − ​ J / ψ ) = ( 1.5 ± 0.3 ± 0.2 ) × 10 − 8 \mathcal{B}_{ee}\mathcal{B}(R\to\pi^{+}\pi^{-}J/\psi)=(1.5\pm 0.3\pm 0.2)\times 10^{-8} and ( 4.8 ± 0.6 ± 0.5 ) × 10 − 8 (4.8\pm 0.6\pm 0.5)\times 10^{-8} for R 1 R_{1} and R 2 R_{2} , respectively, for solution I; and ℬ e ​ e ​ ℬ ​ ( R → π + ​ π − ​ J / ψ ) = ( 3.3 ± 0.7 ± 0.5 ) × 10 − 8 \mathcal{B}_{ee}\mathcal{B}(R\to\pi^{+}\pi^{-}J/\psi)=(3.3\pm 0.7\pm 0.5)\times 10^{-8} and ( 15.3 ± 1.4 ± 1.5 ) × 10 − 8 (15.3\pm 1.4\pm 1.5)\times 10^{-8} for R 1 R_{1} and R 2 R_{2} , respectively, for solution II, where the first and second errors are statistical and systematic, respectively

Cited in the paper.

A smaller systematic error is obtained because we no longer use a BW with a phase-space-dependent total width to parameterize R 1 R_{1}

Cited in the paper.

We perform a partial wave analysis with f 0 ​ ( 500 ) f_{0}(500) , f 0 ​ ( 980 ) f_{0}(980) , non-resonant S-wave, and f 2 ​ ( 1270 ) f_{2}(1270) amplitudes, and find that the S-wave contributions dominate. The MC distributions with fit parameters are shown in Fig. 3

Cited in the paper.

The fraction of Z ​ ( 3900 ) ± Z(3900)^{\pm} events is obtained from a one-dimensional fit to the M max ​ ( π ​ J / ψ ) M_{\mathrm{max}}(\pi J/\psi) distribution without including possible interference with other amplitudes. For a more precise determination of this fraction, a full partial wave analysis with more statistics would be required

Cited in the paper.

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S. Kurokawa and E. Kikutani, Nucl. Instrum. Methods Phys. Res., Sect. A 499

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