Multi-channel joint analysis of the exotic charmonium-like state $T_{c\bar{c}}(4020)$

Abstract

This paper reports the first multi-channel joint analysis to identify the properties of the exotic charmonium-like state $T_{c\bar{c}}(4020)$ via the electron-positron annihilation process $e^{+}e^{-}\toπ^{+}T_{c\bar{c}}(4020)^{-}+c.c$. A partial wave analysis is performed simultaneously in three decay channels $T_{c\bar{c}}(4020)^{-}\to {D}^{*0}D^{*-}$, $π^{-}J/ψ$, and $π^{-}h_{c}$, based on data samples taken at $\sqrt{s}=4.395$ and $4.416\,\mathrm{GeV}$ with an integrated luminosity of $1598.9\,\mathrm{pb}^{-1}$ collected with the BESIII detector operating on the BEPCII collider. For the first time, the spin-parity of the $T_{c\bar{c}}(4020)^{-}$ is determined to be $J^{P}=1^{+}$ with a significance $11.7σ$. Pole positions are extracted on the Riemann sheets with three branch points in the complex energy plane. Furthermore, the relative branching fractions are obtained as $\mathcal{B}[T_{c\bar{c}}(4020)^{-}\toπ^{-}J/ψ]/\mathcal{B}[T_{c\bar{c}}(4020)^{-}\to{D}^{*0}D^{*-}]=(3.6\pm0.6\pm1.6)\times10^{-3}$ and $\mathcal{B}[T_{c\bar{c}}(4020)^{-}\toπ^{-}h_{c}]/\mathcal{B}[T_{c\bar{c}}(4020)^{-}\to{D}^{*0}D^{*-}]=(8.9\pm1.3\pm2.3)\times10^{-2}$, where the first uncertainties are statistical, and the second are systematic.

Figures (11)

• Figure 1: The pole masses and widths of the $T_{c\bar{c}}(4020)$ (also $T_{c\bar{c}}(4025)$) states obtained in the processes of $e^+e^-\to\pi\pi h_{c}$ and $D^{*}\bar{D}^{*}\pi$. Here, PRL indicates the reference Physical Review Letters.
• Figure 2: An illustration and definition of the helicity angles involved in the PWA.
• Figure 3: Mass projections $M(D^{*0}D^{*-})$, $M(D^{*0(-)}\pi^+)$, $M(J/\psi\pi^{\pm})$, $M(h_{c}\pi^{\pm})$, and $M(\pi^+\pi^-)$ of the data compared to the results of the simultaneous fit for the processes of $e^+e^-\to D^{*0}D^{*-}\pi^{+}$, $\pi^{+}\pi^{-}J/\psi$, and $\pi^{+}\pi^{-}h_{c}$ at $\sqrt{s}=4.395$ and $4.416\,\unit{GeV}$. The points with error bars are data, and the black histograms are the total fit results, including backgrounds. The grey-shaded histograms denote backgrounds. The colorful lines correspond to the individual contributions from each component.
• Figure 4: The distributions of the likelihood ratio $t\equiv-2[-\ln L^{1^+}-(-\ln L^{J^P})]$. The black dots denote the toy MC samples generated under the hypothesis of $J^P=1^+$. The red, green, and blue dots represent the samples generated under the hypotheses $J^P=1^-,2^+$, and $2^-$, respectively. The pink-dashed vertical lines show the $t$ values in the data, and the deviations between the toy MC samples and the data are noted on the plots.
• Figure 5: At $\sqrt{s}=4.416\,\unit{GeV}$, the left plot shows the $RQ(D^{0}\pi^0\pi^+)$ distribution in the process $e^+e^-\to D^{*0}D^{*-}\pi^{+}$, where backgrounds are negligible as indicated with the tiny amount of survived inclusive MC events. The middle plot shows the $M(l^{+}l^{-})$ distribution in $e^+e^-\to\pi^{+}\pi^{-}J/\psi$ and the right plot presents the $RM(\pi^+\pi^-)$ distribution in $\pi^{+}\pi^{-}h_{c}$. The signal and sideband regions are marked with red and blue vertical dotted lines, respectively.