Strong and radiative decays of X(3872) as a hadronic molecule with a negative parity

Properties of X(3872) are studied by regarding it as a $DD^{\ast}$ hadronic molecule with $J^{PC} = 2^{-+}$ in the phenomenological Lagrangian approach. We find that our model with about 97.6% isospin zero component explains the existing data nicely, for example, the ratio $\mathcal{B}(X(3872) \to J/ψπ^+π^-π^0)/\mathcal{B}(X(3872) \to J/ψπ^+π^-)$. We predict the partial widths of the radiative decays of $X(3872) \to γJ/ψ$, $γψ(2S)$ and the strong decays of $X(3872) \to J/ψπ^+ π^-$, $J/ψπ^+π^-π^0$ as well as $X(3872) \to χ_{cJ}π^0$. Our analysis shows that the measurement of the ratio $\mathcal{B}(X(3872) \to χ_{c0}π^0)/\mathcal{B}(X(3872) \to χ_{c1}π^0)$ may signal the nature of X(3872).

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