A coupled-channel lattice study on the resonance-like structure $Z_c(3900)$

Abstract

In this exploratory study, near-threshold scattering of $D$ and ${\bar{D}}^{\ast }$ meson is investigated using lattice QCD with $N_f=2+1+1$ twisted mass fermion configurations. The calculation is performed within the coupled-channel Lüscher's finite-size formalism. The study focuses on the channel with $I^G(J^{PC})=1^{+}(1^{+-})$ where the resonance-like structure $Z_c(3900)$ was discovered. We first identify the most relevant two channels of the problem and the lattice study is performed within the two-channel scattering model. Combined with a two-channel Ross-Shaw theory, scattering parameters are extracted from the energy levels by solving the generalized eigenvalue problem. Our results on the scattering length parameters suggest that, at the particular lattice parameters that we studied, the best fitted parameters do not correspond to a peak behavior in the elastic scattering cross section near the threshold. Furthermore, within the zero-range Ross-Shaw theory, the scenario of a narrow resonance close to the threshold is disfavored beyond $3\sigma$ level.

arXiv comment15 pages, 6 figures, minor changes. Version accepted by Chinese Physics C

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Cited by in corpus (12)

• Chiral perturbation theory for heavy hadrons and chiral effective field theory for heavy hadronic molecules
• Towards a theory of hadron resonances
• Charmonium-like resonances with $J^{PC}=0^{++},2^{++}$ in coupled $D\bar{D}$, $D_s{\bar{D}}_s$ scattering on the lattice
• $Z_{cs}(3985{)}^{-}$ as the $U$-spin partner of $Z_c(3900{)}^{-}$ and implication of other states in the ${\text{SU(3)}}_F$ symmetry and heavy quark symmetry
• One Born$-$Oppenheimer Effective Theory to rule them all: hybrids, tetraquarks, pentaquarks, doubly heavy baryons and quarkonium
• Charmonium and Charmoniumlike States at the BESIII Experiment
• Towards the understanding of $Z_c(3900)$ from lattice QCD
• $Z_c$ and $Z_{cs}$ systems with operator mixing at NLO in QCD sum rules
• Charmoniumlike Channels $1^{+}$ with Isospin $1$ from Lattice and Effective Field Theory
• Effective range expansion with a long-range force
• Construction of general $N$-body lattice operators with arbitrary momenta
• QCD confronts heavy-flavor and exotic hadrons