About the exotic structure of $Z_{cs}$

Abstract

Very recently a new hadronic structure around $3.98$ GeV was observed in BESIII experiment. From its decay modes, it is reasonable for people to assign it to the category of exotic state, say $Z^+_{cs}$, the stranged-parter of $Z_{c}(3900)$. This finding indicates for the first time the exotic state with strange quark in charm sector, and hence has a peculiar importance. By virtue of the QCD Sum Rule technique, we analyze the $Z^+_{cs}$ about its possible configuration and physical properties, and find it could be configured as a mixture of two types of structures, $[1_c]_{\bar{c} u}\otimes[1_c]_{\bar{s} c}$ and $[1_c]_{\bar{c} c}\otimes[1_c]_{\bar{s} u}$, or $[3_c]_{\bar{c} u}\otimes[\bar{3}_c]_{\bar{s} c}$ and $[3_c]_{\bar{c} c}\otimes[\bar{3}_c]_{\bar{s} u}$, with $J^P=1^+$. Physically, it then appears to be the emergence of a compound of four possible currents in each configuration, which tells the single current evaluation of hadron spectroscopy and their decay properties are sometimes not enough. We find in both cases the energy spectra may fit well with the experimental observation, i.e. $3.98$ GeV, within the uncertainties, while noted the former is not favored by vector meson exchange model. Various $Z^+_{cs}(3980)$ decay modes are evaluated, which are critical for pinning down its configuration and left for experimental verification. We also predict the mass of $Z^0_{cs}$, the neutral partner of $Z^+_{cs}(3980)$, and analyze its dominant decay probabilities.