Deciphering the charged heavy quarkoniumlike states in chiral effective field theory

Abstract

We generalize the framework of chiral effective field theory to study the interactions of the isovector $D^{\ast }{\bar{D}}^{(\ast )}$ and $B^{\ast }{\bar{B}}^{(\ast )}$ systems up to the next-to-leading order, in which the long-, mid-, and short-range force contributions as well as the $S$-$D$ wave mixing are incorporated. Based on the Lippmann-Schwinger equation, we fit the invariant mass distributions of the elastic channels measured by the BESIII and Belle Collaborations. Our results indicate that the four charged charmoniumlike and bottomoniumlike states $Z_c(3900)$, $Z_c(4020)$ and $Z_b(10610)$, $Z_b(10650)$ can be well identified as the $D{\bar{D}}^{\ast },D^{\ast }{\bar{D}}^{\ast }$ and $B{\bar{B}}^{\ast },B^{\ast }{\bar{B}}^{\ast }$ molecular resonances. The bound state explanations are vetoed in our framework. Our study favors the $Z_c$ and $Z_b$ states are the twin partners under the heavy quark symmetry.

Comments: 6 pages, 3 figures and 1 table