Charmoniumlike channels 1+ with isospin 1 from lattice and effective field theory

Abstract

Many exotic charmoniumlike mesons have already been discovered experimentally, of which the Zc mesons with isospin 1 are prominent examples. We investigate JPC=1+± states with flavor c¯cq¯q (q=u, d) in isospin 1 using lattice QCD. This is the first study of these mesons employing more than one volume and involving frames with nonzero total momentum. We utilize two Nf=2+1 CLS ensembles with mπ≃280 MeV. The simulations are performed with unphysical light quark masses at a single lattice spacing of a≃0.086 fm and omit ψ(2S)π, ψ(3770)π and three-particle decay channels, so our results provide only qualitative insights. Resulting eigenenergies are compatible or just slightly shifted down with respect to noninteracting energies, where the most significant shifts occur for certain DD¯* states. Both channels 1+± have a virtual pole slightly below the threshold if DD¯* is assumed to be decoupled from other channels. In addition, we perform a coupled channel analysis of J/ψπ and DD¯* scattering with JPC=1+− within an effective field theory framework. The J/ψπ and DD¯* invariant-mass distributions from BESIII and finite-volume energies from several lattice QCD simulations, including this work, are fitted simultaneously. All fits yield two poles relatively close to the DD¯* threshold and reasonably reproduce the experimental Zc peaks. They also reproduce lattice energies up to slightly above the DD¯* threshold, while reproduction at even higher energies is better for fits that put more weight on the lattice data. Our findings suggest that the employed effective field theory can reasonably reconcile the peaks in the experimental line shapes and the lattice energies, although those lie close to noninteracting energies. We also study J/ψπ scattering in s wave and place upper bounds on the phase shift. Published by the American Physical Society 2025