$\bar{D}^{(*)}_{s}D^{(*)}$ molecular state with $J^{P}=1^{+}$

TL;DR

This paper constructs a molecular state model for the $Z_{cs}(3985)$, calculates its properties using QCD sum rules, and finds results consistent with experimental measurements, aiding understanding of its internal structure.

Contribution

It introduces a novel molecular state model for $Z_{cs}(3985)$ and computes its mass, magnetic moment, and decay widths using advanced QCD sum rule techniques.

Findings

Mass agrees with BESIII measurements

Decay widths are compatible with experimental data

Magnetic moment provides insight into internal structure

Abstract

In this paper, we construct $\bar{D}^{(*)}_{s}D^{(*)}$-molecule-type interpolating currents $J_{(\pm)\mu}(x)$ with $J^{P}=1^{+}$, calculate the corresponding mass and magnetic moment using the QCD sum rule method and its extension in the weak electromagnetic field, and study the processes of $Z_{(\pm)cs}$ to $\eta_{c}K^{*}$, $J/\psi K$, $\bar{D}D^{*}_{s}$, and $\bar{D}^{*}D_{s}$ via three-point sum rules. The numerical values are $m_{Z_{(\pm)cs}}=3.99^{+0.17}_{-0.14}~\mbox{GeV}$, and $\lambda_{Z_{(\pm)cs}}=2.07^{+0.28}_{-0.16}\times10^{-2}~\mbox{GeV}^{5}$, $\mu_{Z_{(\pm)cs}}=0.18^{+0.16}_{-0.09}~\mu_{N}$ with $\mu_{N}$ the nucleon magneton, $\Gamma_{Z_{(+)cs}}=17.47^{+12.70}_{-8.08}$, and $\Gamma_{Z_{(-)cs}}=13.86^{+10.37}_{-6.51}$. The masses are in agreement with the recently measured value of $Z_{cs}(3985)$ by the BESIII Collaboration, $m^{exp}_{Z_{cs}}=(3982.5^{+1.8}_{-2.6}\pm2.1)~\mbox{MeV}$. The widths are compatible with the experimental value, $\Gamma^{exp}_{Z_{cs}}=(12.8^{+5.3}_{-4.4}\pm3.0)~\mbox{MeV}$. The magnetic moment and the various decay modes can help us to determine the inner structure of $Z_{cs}(3985)$ when being confronted with experimental data in the future.