Coupled-Channel Analysis of the ${\chi }_{c1}(3872)$ Line Shape with BESIII Data

We perform a study of the ${\chi }_{c1}(3872)$ line shape using the data samples of $e^{+}{e}^{-}\to \gamma {\chi }_{c1}(3872)$, ${\chi }_{c1}(3872)\to D^0{\overline{D}}^0{\pi }^0$, and ${\pi }^{+}{\pi }^{-}J/\psi$ collected with the BESIII detector. The effects of the coupled channels and the off-shell $D^{*0}$ are included in the parametrization of the line shape. The line shape mass parameter is obtained to be $M_X=(3871.63\pm 0.13_{-0.05}^{+0.06})\mathrm{MeV}$. Two poles are found on the first and second Riemann sheets corresponding to the $D^{*0}{\overline{D}}^0$ branch cut. The pole location on the first sheet is much closer to the $D^{*0}{\overline{D}}^0$ threshold than the other, and is determined to be $7.04\pm 0.15_{-0.08}^{+0.07}\mathrm{MeV}$ above the $D^0{\overline{D}}^0{\pi }^0$ threshold with an imaginary part $-0.19\pm 0.08_{-0.19}^{+0.14}\mathrm{MeV}$.

Figure 1

Distributions of (a) $D^0{\overline{D}}^0{\pi }^0$ and (b) ${\pi }^{+}{\pi }^{-}J/\psi$ invariant mass. The black dots with error bars are the data from Ref. [19]; the blue continuous lines are the probability density functions at the best estimation; the red dotted lines are the signal shapes; the green dashed lines are the background shapes; and the black dashed lines represent the line shape without the mass resolution considered, normalized to the signal height for comparison. (c) The ${\chi }_{c1}(3872)$ line shape at the best estimation. Here, $d\mathrm{Br}/dE$ is $(g\times k_{\mathrm{eff}}+{\mathrm{\Gamma }}_0)/|D(E){|}^2$ in arbitrary units (a.u.). The cyan shaded band indicates the statistical uncertainty and the vertical dashed line indicates the position of the $D^{*0}{\overline{D}}^0$ threshold.

Figure 2

The phase of the amplitude on (a) Sheet I and (b) Sheet II with respect to complex energy. The solid cyan line starting from the point 7.033–0.027i MeV is the branch cut, the dashed cyan line is the real axis and the red trajectory approaching the real axis is obtained by continuously decreasing ${\mathrm{\Gamma }}_0$ to 0. (c) The phase of the amplitude with respect to $k$. The upper (lower) half-plane corresponds to Sheet I (Sheet II).