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

TL;DR

This lattice QCD study searches for the $Z_c^+$ hadron below 4.2 GeV, finding no clear candidate but discussing the challenges and potential methods to identify such exotic states.

Contribution

The paper applies lattice QCD with various interpolating fields to investigate the $Z_c^+$ channel, highlighting the difficulties in detecting exotic states amidst two-meson backgrounds.

Findings

All expected two-meson states are observed.

No additional $Z_c^+$ candidate found below 4.2 GeV.

Inclusion of two-meson interpolators affects candidate robustness.

Abstract

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.