Low-energy Scattering of $(D{\bar{D}}^{\ast }{)}^{\pm }$ System And the Resonance-like Structure $Z_c(3900)$

Abstract

In this exploratory lattice study, low-energy scattering of the $(D{\bar{D}}^{\ast }{)}^{\pm }$ meson system is analyzed using lattice QCD with $N_f=2$ twisted mass fermion configurations with three pion mass values. The calculation is performed within single-channel Lüscher's finite-size formalism. The threshold scattering parameters, namely the scattering length $a_0$ and the effective range $r_0$, for the $s$-wave scattering in $J^P=1^{+}$ channel are extracted. For the cases in our study, the interaction between the two charmed mesons is weakly repulsive. Our lattice results therefore do not support the possibility of a shallow bound state for the two mesons for the pion mass values we studied. This calculation provides some useful information on the nature of the newly discovered resonance-like structure $Z_c(3900)$ by various experimental groups.

Comments: 14 pages, 6 figures. Version accepted by PRD