Simple Explanation for the $X(3872)$ Mass Shift Observed in the Decay $X(3872)\to D^{*0}{\overline{D}}^0$

We propose a simple explanation for the increase of approximately $3\mathrm{MeV}/c^2$ in the mass value of the $X(3872)$ obtained from $D^{*0}{\overline{D}}^0$ decay relative to that obtained from decay to $J/\psi {\pi }^{+}{\pi }^{-}$. If the total width of the $X(3872)$ is 2–3 MeV, the peak position in the $D^{*0}{\overline{D}}^0$ invariant mass distribution is sensitive to the final state orbital angular momentum because of the proximity of the $X(3872)$ to $D^{*0}{\overline{D}}^0$ threshold. We show that for total width 3 MeV and one unit of orbital angular momentum, a mass shift $\sim 3\mathrm{MeV}/c^2$ is obtained; experimental mass resolution should slightly increase this value. A consequence is that spin-parity $2^{-}$ is favored for the $X(3872)$.

Figure 1

(a) The $m(D^{*0}{\overline{D}}^0)$ line shape obtained from Eq. (11) for $J^P=1^{+}$ using $X(3872)$ mass $3871.4\mathrm{MeV}/c^2$ (indicated by the dot-dashed line) and width 3 MeV. (b) The histogram for 3000 events generated using the curve shown in (a).

Figure 2

(a) The $m(D^{*0}{\overline{D}}^0)$ line shape obtained from Eq. (11) for $J^P=2^{-}$ using $X(3872)$ mass $3871.4\mathrm{MeV}/c^2$ (indicated by the dot-dashed line) and width 3 MeV. (b) The histogram for 3000 events generated using the curve shown in (a).