$D$-wave dimeson resonance interpretation to the $Z_c/Z_{cs}/Z_b$ states

TL;DR

This paper models $D$-wave meson interactions at various orders, predicting resonances that align with observed exotic states, suggesting a unified $D$-wave resonance interpretation for several $Z$ states.

Contribution

It introduces a comprehensive $D$-wave interaction framework at multiple orders, successfully matching experimental resonance parameters and proposing a unified interpretation for $Z$ states.

Findings

Predicted $P$-wave resonance near $G(3900)$.

Identified $D$-wave resonances consistent with $Z_c$ and $Z_b$ states.

Reproduced broad widths of $Z_{cs}(4000)$ and $Z_{cs}(4220)$.

Abstract

In this work, we construct the $S$-wave, $P$-wave, and $D$-wave $D^{(*)}\bar{D}^{*}_{(s)}$/$B^{(*)}\bar{B}^{*}_{(s)}$ interactions by considering the lowest order contributions from the leading order (LO), next-to-leading order (NLO), and next-to-next-to-next-to-leading order (N$^3$LO) contact terms, respectively. After solving the corresponding Lippmann-Schwinger equation (LSE), we obtain the typical pole trajectory for the $S$-wave/$P$-wave/$D$-wave state. We adjust the $P$-wave low energy constant (LEC) and {accordingly obtain a $P$-wave $D\bar{D}^*/D^*\bar{D}$} resonance state that may correspond to the observed $G(3900)$, { and its $P$-wave $D^*\bar{D}^*$ and $B^{(*)}\bar{B}^{*}$ partners are also predicted}. Then we proceed to adjust the $D$-wave LECs to looking for the $D$-wave $D^{(*)}\bar{D}^{(*)}_{(s)}$/$B^{(*)}\bar{B}^{(*)}_{(s)}$ resonances. The satisfactory consistencies between our results { and the experimental resonance parameters} of $Z_c(3900)$/$Z_c(4020)$, $Z_b(10610)$/$Z_b(10650)$, and $Z_{cs}(4000)$/$Z_{cs}(4220)$ indicate that the $D$-wave resonance interpretation may provide a unified picture to understand these { isovector charmoniumlike states. Especially, the broad width features of $Z_{cs}(4000)$ and $Z_{cs}(4220)$ can be naturally reproduced by interpreting them as $D$-wave $D\bar{D}_s^*$ and $D^*\bar{D}_s^*$ resonances, respectively.