Low-energy $D^{*+}D^0_1$ Scattering and the Resonance-like Structure $Z^+(4430)$

Low-energy scattering of $D^*$ and $D_1$ meson are studied using quenched lattice QCD with improved lattice actions on anisotropic lattices. The calculation is performed within L\"uscher's finite-size formalism which establishes the relation between the scattering phase in the infinite volume and the exact energy level in the finite volume. The threshold scattering parameters, namely the scattering length $a_0$ and the effective range $r_0$, for the s-wave scattering in $J^P=0^-$ channel are extracted. After the chiral and continuum extrapolations, we obtain: $a_0=2.52(47)$fm and $r_0=0.7(1)$fm where the errors are purely statistical. Based on these results, we discuss the possibility of a shallow bound state for the two charmed mesons within the non-relativistic potential scattering model. It is argued that, albeit the interaction between the two charmed mesons being attractive, it is unlikely that they can form a shallow bound state in this channel. This calculation provides some useful information on the nature of the newly discovered resonance-like structure $Z^+(4430)$ by the Belle Collaboration.