Analysis ofJ/ψπ+π−andD0D¯0π0decays of theX(3872)

Abstract

We analyze recent data from the BABAR and Belle Collaborations on the $X(3872)$ resonance in the $J/\ensuremath{\psi}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ and ${D}^{0}{\overline{D}}^{0}{\ensuremath{\pi}}^{0}$ decay channels, taking careful account of the universal features of an $S$-wave threshold resonance. Because the line shapes for such a resonance are not integrable functions of the energy, the resonance parameters depend on the prescriptions used to define them. In recent experimental analyses of the ${D}^{0}{\overline{D}}^{0}{\ensuremath{\pi}}^{0}$ channel, an event near the ${D}^{*0}{\overline{D}}^{0}$ threshold was assumed to come from ${D}^{*0}{\overline{D}}^{0}$ or ${D}^{0}{\overline{D}}^{*0}$ and was therefore assigned an energy above the threshold. Taking this effect into account, our analysis of the ${D}^{0}{\overline{D}}^{0}{\ensuremath{\pi}}^{0}$ data gives a mass for the $X(3872)$ that is below the ${D}^{*0}{\overline{D}}^{0}$ threshold. Our analyses in both the $J/\ensuremath{\psi}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ and ${D}^{0}{\overline{D}}^{0}{\ensuremath{\pi}}^{0}$ channels are consistent with the identification of the $X(3872)$ as an extremely weakly bound charm meson molecule.