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

Recently experimentalists have discovered several charged charmonium-like hadrons $Z_c^{+}$ with unconventional quark content $\bar{c}c\bar{d}u$. 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 $J\mathrm{/}\psi \pi$, ${\psi }_{2S}\pi$, ${\psi }_{1D}\pi$, $D\bar D^$,$D^\bar D^*$,$\eta_c\rho$ 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.