A coupled-channel analysis of the $X(3872)$ lineshape with BESIII data

Abstract

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