Observation of $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}\psi (3770)$ and $D_1(2420{)}^0{\overline{D}}^0+\mathrm{c}.\mathrm{c}.$

Several intermediate states of the reaction channels $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{D}^0{\overline{D}}^0$ and $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{D}^{+}{D}^{-}$ are studied using the data samples collected with the BESIII detector at center-of-mass energies above 4.08 GeV. For the first time in this final state, a $\psi (3770)$ signal is seen in the $D\overline{D}$ invariant mass spectrum, with a statistical significance of $5.2\sigma$ at $\sqrt{s}=4.42\mathrm{GeV}$. There is also evidence for this resonance at $\sqrt{s}=4.26$ and 4.36 GeV with statistical significance of $3.2\sigma$ and $3.3\sigma$, respectively. In addition, the Born cross section of $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}\psi (3770)$ is measured. The proposed heavy-quark-spin-symmetry partner of the $X(3872)$, the state $X_2(4013)$, is also searched for in the $D\overline{D}$ invariant mass spectra. No obvious signal is found. The upper limit of the Born cross section of the process $e^{+}{e}^{-}\to {\rho }^0{X}_2(4013)$ combined with the branching fraction is measured. Also, the processes $e^{+}{e}^{-}\to D_1(2420)\overline{D}+\mathrm{c}.\mathrm{c}.$ are investigated. The neutral mode with $D_1(2420{)}^0\to D^0{\pi }^{+}{\pi }^{-}$ is reported with statistical significance of $7.4\sigma$ at $\sqrt{s}=4.42\mathrm{GeV}$ for the first time, and evidence with statistical significance of $3.2\sigma$ and $3.3\sigma$ at $\sqrt{s}=4.36$ and 4.60 GeV is seen, respectively. No evident signal for the process $e^{+}{e}^{-}\to D_1(2420{)}^0{\overline{D}}^0+\mathrm{c}.\mathrm{c}.,D_1(2420{)}^0\to D^{*+}{\pi }^{-}$ is reported. Evidence for $e^{+}{e}^{-}\to D_1(2420{)}^{+}{D}^{-}+\mathrm{c}.\mathrm{c}.,D_1(2420{)}^{+}\to D^{+}{\pi }^{+}{\pi }^{-}$ is reported with statistical significance of $3.1\sigma$ and $3.0\sigma$ at $\sqrt{s}=4.36$ and 4.42 GeV, respectively.

Figure 1

Scatter plots of the invariant masses of $D^0$ versus ${\overline{D}}^0$ meson candidates (a) and the invariant masses of $D^{+}$ versus $D^{-}$ meson candidates (b) at $\sqrt{s}=4.42\mathrm{GeV}$. The rectangles show the signal regions (red solid lines) and sideband regions (pink dotted lines).

Figure 2

Distributions of the invariant masses $M(D^0{\pi }^{+})$ (a) and $M({\overline{D}}^0{\pi }^{-})$ (b) at $\sqrt{s}=4.42\mathrm{GeV}$. The black dots with error bars are data and the blue solid lines are the fit results. The brown dashed lines are the distributions from ${\overline{D}}^0{D}_1^0$ and the green long-dashed lines the distributions from ${\pi }^{+}{\pi }^{-}\psi (3770)$. The pink dotted-dotted-dashed lines show the distribution from ${\pi }^{+}{\pi }^{-}{X}_2(4013)$. The distributions from ${\overline{D}}^0{D}_1^0$ are normalized to the maximum bin content of data, and the distributions from ${\pi }^{+}{\pi }^{-}\psi (3770)$ and ${\pi }^{+}{\pi }^{-}{X}_2(4013)$ are normalized arbitrarily.

Figure 3

Fit to the $D\overline{D}$ invariant mass distribution at $\sqrt{s}=4.26$ (a), 4.36 (b), and 4.42 (c) GeV. The black dots with error bars are data and the blue solid lines are the fit results. The red long-dashed lines indicate the contribution of the $\psi (3770)$ and the pink dashed lines the contribution of the $D_1(2420)\overline{D}$ final state. The brown dotted-dashed lines show the ${\pi }^{+}{\pi }^{-}D\overline{D}$ background contributions and the green shaded histograms are the distributions from the sideband regions.

Figure 4

Distribution of the $M({\pi }^{\pm }\psi (3770))$ invariant mass at $\sqrt{s}=4.26$ (a), 4.36 (b), 4.42 (c) GeV. The black dots with error bars are data. The blue histograms show the distributions of the MC simulation of the process $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}\psi (3770)$ (phase space distributed), while the green shaded histograms are the distributions from the sideband regions.

Figure 5

Fit to the region of large $D\overline{D}$ invariant masses at $\sqrt{s}=4.36$ (a), 4.42 (b), and 4.60 (c) GeV. The black dots with error bars are data, the blue solid curves are the fit results, the pink long-dashed lines show the X(4013) signal contribution and the green dashed lines describe the background distribution.

Figure 6

Fit to the $D^0{\pi }^{+}{\pi }^{-}$ (first row), $D^{*+}{\pi }^{-}$ (second row) and $D^{+}{\pi }^{+}{\pi }^{-}$ (third row) invariant mass distribution at $\sqrt{s}=4.36$ (a, d, g), 4.42 (b, e, h), and 4.60 (c, f, i) GeV. The black dots with error bars are data, the blue solid curves the fit results, and the red long-dashed lines the $D_1(2420)$ signal contributions. The pink dashed lines are the contributions of the final state ${\pi }^{+}{\pi }^{-}\psi (3770)$, the blue dotted-dashed lines these of the ${\pi }^{+}{\pi }^{-}D\overline{D}$ or $D_2^{*}(2460{)}^0\overline{D}$ final state, and the light blue dotted-long-dashed lines the $D^{*}\overline{D}\pi$ background contributions, while the green shaded histograms are the distributions from the sideband regions.

Figure 7

Born cross sections of the processes (black dots) $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}\psi (3770)$ (a), $e^{+}{e}^{-}\to D_1(2420{)}^0{\overline{D}}^0\to {\pi }^{+}{\pi }^{-}{D}^0{\overline{D}}^0$ (b), $e^{+}{e}^{-}\to D_1(2420{)}^0{\overline{D}}^0\to D^{*+}{\overline{D}}^0{\pi }^{-}\to {\pi }^{+}{\pi }^{-}{D}^0{\overline{D}}^0$ (c), and $e^{+}{e}^{-}\to D_1(2420{)}^{+}{D}^{-}\to {\pi }^{+}{\pi }^{-}{D}^{+}{D}^{-}$ (d). The error bars include the statistical and systematic uncertainties. The red triangles are the upper limits on the Born cross sections at the 90% C.L.

Figure 8

Fit to the $D\overline{D}$ invariant mass distribution at $\sqrt{s}=4.09$ (a), 4.19 (b), 4.21 (c), 4.22 (d), 4.23 (e), 4.24 (f), 4.26 (g), 4.31 (h), 4.36 (i), 4.39 (j), 4.42 (k), 4.47 (l), 4.53 (m), 4.57 (n), and 4.60 (o) GeV. The black dots with error bars are data and the blue solid lines are the fit results. The red long-dashed lines indicate the contribution of the $\psi (3770)$ and the pink dashed lines the contribution of the $D_1(2420)\overline{D}$ final state. The brown dotted-dashed lines show the ${\pi }^{+}{\pi }^{-}D\overline{D}$ background contributions and the green shaded histograms are the distributions from the sideband regions.

Figure 9

Fit to the $D^0{\pi }^{+}{\pi }^{-}$ invariant mass distribution at $\sqrt{s}=4.31$ (a), 4.36 (b), 4.39 (c), 4.42 (d), 4.47 (e), 4.53 (f), 4.57 (g), and 4.60 (h) GeV. The black dots with error bars are data, the blue solid curves the fits results, and the red long-dashed lines the $D_1(2420)$ signal contributions. The pink dashed lines are the contributions of the final state ${\pi }^{+}{\pi }^{-}\psi (3770)$ and the blue dot-dot-dashed lines these of the ${\pi }^{+}{\pi }^{-}D\overline{D}$ final state, while the green shaded histograms are the distributions from the sidebands regions.

Figure 10

Fit to the $D^{*+}{\pi }^{-}$ invariant mass distribution at $\sqrt{s}=4.31$ (a), 4.36 (b), 4.39 (c), 4.42 (d), 4.47 (e), 4.53 (f), 4.57 (g), and 4.60 (h) GeV. The black dots with error bars are data, the blue solid curves the fit results, and the red long-dashed lines the $D_1(2420)$ signal contributions. The light blue dot-long-dashed lines are the $D^{*}\overline{D}\pi$ and the blue dot-dashed lines the $D_2^{*}(2460{)}^0\overline{D}$ background contributions, while the green shaded histograms are the distributions from the sideband regions.

Figure 11

Fit to the $D^{+}{\pi }^{+}{\pi }^{-}$ invariant mass distribution at $\sqrt{s}=4.31$ (a), 4.36 (b), 4.39 (c), 4.42 (d), 4.47 (e), 4.53 (f), 4.57 (g), and 4.60 (h) GeV. The black dots with error bars are data, the blue solid curves the fit results, and the red long-dashed lines the $D_1(2420)$ signal contribution. The pink dashed lines are contributions of the final state ${\pi }^{+}{\pi }^{-}\psi (3770)$ and the blue dot-dot-dashed lines these of the ${\pi }^{+}{\pi }^{-}D\overline{D}$ final state, while the green shaded histograms are the distributions from the sideband regions.