Abstract
The hidden-charm tetraquarks with strangeness, $c\bar{c}s\bar{q}$ $(q=u,\,d)$, in $J^P=0^+$, $1^+$ and $2^+$ are systematically investigated in the framework of real- and complex-scaling range of a chiral quark model, whose parameters have been fixed in advance describing hadron, hadron-hadron and multiquark phenomenology. Each tetraquark configuration, compatible with the quantum numbers studied, is taken into account; this includes meson-meson, diquark-antidiquark and K-type arrangements of quarks with all possible color wave functions in four-body sector. Among the different numerical techniques to solve the Schr\"odinger-like 4-body bound state equation, we use a variational method in which the trial wave function is expanded in complex-range Gaussian basis functions, which is characterized by its simplicity and flexibility. This theoretical framework has already been used to study different kinds of multiquark systems, such as the hidden-charm pentaquarks, $P^+_c$, and doubly-charmed tetraquarks, $T^+_{cc}$. The recently reported $Z_{cs}$ states by the BESIII and LHCb collaborations are generally compatible with either compact tetraquark or hadronic molecular resonance configurations in our investigation. Moreover, several additional exotic resonances are found in the mass range between 3.8 GeV and 4.6 GeV.
Highlights
A structure with a significance of 5.3σ was reported in the process of eþe− → KþðD−s DÃ0 þ DÃs−D0Þ by the BESIII Collaboration [1]; its experimentally measured mass and width were 3982.5þ−21..68 Æ 2.1 and 12.8þ−45..43 Æ 3.0 MeV, respectively
The hidden-charm tetraquarks with strangeness, ccsq (q 1⁄4 u, d), in JP 1⁄4 0þ, 1þ, and 2þ are systematically investigated in the framework of real- and complex-scaling range of a chiral quark model, whose parameters have been fixed in advance describing hadron, hadron-hadron, and multiquark phenomenology
Among the different numerical techniques to solve the Schrödinger-like four-body bound state equation, we use a variational method in which the trial wave function is expanded in complex-range Gaussian basis functions, which is characterized by its simplicity and flexibility
Summary
A structure with a significance of 5.3σ was reported in the process of eþe− → KþðD−s DÃ0 þ DÃs−D0Þ by the BESIII Collaboration [1]; its experimentally measured mass and width were 3982.5þ−21..68 Æ 2.1 and 12.8þ−45..43 Æ 3.0 MeV, respectively. The Zcsð4220Þ and Xð4630Þ are reported with significance exceeding 5σ derivations These facts trigger many theoretical investigations on the nature of hidden-charm tetraquark with strangeness. The DÃDs − DD Ãs and DÃD Ãs molecules with spin-parity JP 1⁄4 1þ state can be related to the mentioned ZðcÃsÞ particles [3]. This result is supported by a coupled-channel calculation [4], a variety of effective field theory frameworks [5,6,7,8], approaches based on QCD sum rules [9,10], and potential model descriptions [11]. The two- and four-body configuration mixing scheme for describing the Zcsð3985Þ state has been proposed to be crucial in many theoretical investigations; viz. the Zcsð3985Þ is excluded as a pure DÃ0D−s =D0DÃs−=DÃ0DÃs− hadronic molecular state in, for instance, the one-bosonexchange model [13,14] and constituent quark model [15]
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