Simple Explanation for the X(3872) Mass Shift Observed in the Decay X(3872)→D^*0D̅ ⁰

We propose a simple explanation for the increase of approximately 3  MeV/c² in the mass value of the X(3872) obtained from D^*0D̅ ⁰ decay relative to that obtained from decay to J/ψπ⁺π^-. If the total width of the X(3872) is 2–3 MeV, the peak position in the D^*0D̅ ⁰ invariant mass distribution is sensitive to the final state orbital angular momentum because of the proximity of the X(3872) to D^*0D̅ ⁰ threshold. We show that for total width 3 MeV and one unit of orbital angular momentum, a mass shift ∼3  MeV/c² is obtained; experimental mass resolution should slightly increase this value. A consequence is that spin-parity 2^- is favored for the X(3872).