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

We perform a study of the $X(3872)$ lineshape using the data samples of $e^+e^-\toγX(3872)$, $X(3872)\to D^0\bar{D}^0 π^0$ and $π^+π^- J/ψ$ collected with the BESIII detector. The effects of the coupled-channels and the off-shell $D^{*0}$ are included in the parameterization of the lineshape. The lineshape mass parameter is obtained to be $M_{X}=(3871.63\pm 0.13^{+0.06}_{-0.05})$ MeV. Two poles are found on the first and second Riemann sheets corresponding to the $D^{*0}\bar{D}^0$ branch cut. The pole location on the first sheet is much closer to the $D^{*0}\bar{D}^0$ threshold than the other, and is determined to be $7.04\pm0.15^{+0.07}_{-0.08}$ MeV above the $D^0\bar{D}^0π^0$ threshold with an imaginary part $-0.19\pm0.08^{+0.14}_{-0.19}$ MeV.