Study of the $Z_c^+$ channel using lattice QCD

Recently experimentalists have discovered several charged charmonium-like hadrons $Z_c^+$ with unconventional quark content $\bar cc\bar d u$. We perform a search for $Z_c^+$ with mass below $4.2~$GeV in the channel $I^G(J^{PC})=1^+(1^{+-})$ using lattice QCD. The major challenge is presented by the two-meson states $J/\psi\, \pi$, $\psi_{2S}\pi$, $\psi_{1D}\pi$, $D\bar D^*$, $D^*\bar D^*$, $\eta_c\rho$ that are inevitably present in this channel. The spectrum of eigenstates is extracted using a number of meson-meson and diquark-antidiquark interpolating fields. For our pion mass of 266~MeV we find all the expected two-meson states but no additional candidate for $Z_c^+$ below $4.2~$GeV. Possible reasons for not seeing an additional eigenstate related to $Z_c^+$ are discussed. We also illustrate how a simulation incorporating interpolators with a structure resembling low-lying two-mesons states seems to render a $Z_c^+$ candidate, which is however not robust after further two-meson states around $4.2~$GeV are implemented.