Study of the resonance structures in the process $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}J/\psi$

Using about $23\mathrm{f}{\mathrm{b}}^{-1}$ of data collected with the BESIII detector operating at the BEPCII storage ring, a precise measurement of the $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}J/\psi$ Born cross section is performed at center-of-mass energies from 3.7730 to 4.7008 GeV. Two structures, identified as the $Y(4220)$ and the $Y(4320)$ states, are observed in the energy-dependent cross section with a significance larger than $10\sigma$. The masses and widths of the two structures are determined to be ($M,\mathrm{\Gamma })=(4221.4\pm 1.5\pm 2.0\mathrm{MeV}/c^2,41.8\pm 2.9\pm 2.7\mathrm{MeV})$ and $(M,\mathrm{\Gamma })=(4298\pm 12\pm 26\mathrm{MeV}/c^2,127\pm 17\pm 10\mathrm{MeV})$, respectively. A small enhancement around 4.5 GeV with a significance about $3\sigma$, compatible with the $\psi (4415)$, might also indicate the presence of an additional resonance in the spectrum. The inclusion of this additional contribution in the fit to the cross section affects the resonance parameters of the $Y(4320)$ state.

Figure 1

Cosine of the polar angle of the $e^{+}$ ($\cos ({\theta }_{e^{+}})$) and $e^{-}$ ($\cos ({\theta }_{e^{-}})$) from the sample at $\sqrt{s}=4.1780\mathrm{GeV}$. The blue dots with error bars are data from the signal region ($3.08<M({\ell }^{+}{\ell }^{-})<3.12\mathrm{GeV}/c^2$). The black line is the signal MC, which is normalized to the number of signal events. The green line comes from the sideband region ($3.02<M({\ell }^{+}{\ell }^{-})<3.06\mathrm{GeV}/c^2$ or $3.14<M({\ell }^{+}{\ell }^{-})<3.18\mathrm{GeV}/c^2$, with an event weight of 0.5) of $M({\ell }^{+}{\ell }^{-})$. The yellow-filled area is the background MC (two-photon process MC), and it is normalized to the number of events in the sideband area. The red line is the sum of signal MC plus background MC simulation.

Figure 2

The variables used in the BDT. (a, b) Distribution of the difference between the measured value and the expected value from the TOF of the two pions. (c, d) The energy deposited in the EMC by the two pions. (e, f) The cosine of the polar angle of $e^{+}$ [$\cos ({\theta }_{e^{+}})$] and ${\pi }^{+}$ [$\cos ({\theta }_{{\pi }^{+}})$]. (g, h) Distributions of ${\chi }_{{\pi }^{+}}$ and ${\chi }_{{\pi }^{-}}$. The blue line is for the signal and the red line for the background. In (a, b, c, d), the peak at $-1.0$ corresponds to the tracks without TOF or EMC information. The background and the signal have the same magnitude. All the distributions come from the signal MC and background MC simulation.

Figure 3

(a,b) The linear correlation coefficients of the variables in the BDT training: (a) is for signal MC and (b) is for background MC simulation samples. (c) The overtraining check of the classifier: the training samples and test samples are in good agreement. (d) The optimized results of the sample at $\sqrt{s}=4.1780\mathrm{GeV}$. The numbers of signal and background events estimated from the data are used to maximize $S/\sqrt{S+B}$ and thus optimize the event selection criteria.

Figure 4

The (a) and (b) plots show the fit results of the invariant mass of the $e^{+}{e}^{-}$ mode and ${\mu }^{+}{\mu }^{-}$ mode, respectively. The (c) and (d) are the two-dimensional distributions of the squared invariant mass of the ${\pi }^{+}{\pi }^{-}$ and ${\pi }^{+}J/\psi$ pairs. Here, (c) is the data, (d) is the MC simulation from PWA. The contents shown come from the sample at $\sqrt{s}=4.1780\mathrm{GeV}$.

Figure 5

Fit to the energy-dependent cross section of $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}J/\psi$ using two different fit models: Model I (a) and Model II (b). The upper panels show the data points with error bars overlaid with the fit result represented by the solid (blue) line. The lower panels show the corresponding fit quality for each data point in terms of $\chi$ in units of $\sigma$. The point of $\sqrt{s}=3.8713\mathrm{GeV}$ is not included in the fit. For more details of the fit models, see the text.

Figure 6

Fit to the energy-dependent cross section of the process $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}J/\psi$, where an additional BW function is added based on Model I. The upper panels show the data points with error bars overlaid with the fit result represented by the solid (blue) line. The lower panels show the corresponding fit quality for each data point in terms of $\chi$ in units of $\sigma$, and the fit results are listed in Table 3. (a) and (b): The new BW function with free parameters. (c) and (d): The new BW function with parameters fixed to the $\psi (4415)$ and $Y(4500)$ resonance parameters. The point of $\sqrt{s}=3.8713\mathrm{GeV}$ is not included in the fit.