The decay widths of the $Z_{cs}(3985/4000)$ based on rigorous quark-hadron duality

Abstract

In this work, we explore the hadronic coupling constants G ZJ/ψK , GZη cK * , G ZD * Ds of the exotic states Zcs(3985/4000) both in the pictures of the tetraquark states and molecular states with the tentative assignments J P C = 1 +− based on the rigorous quark-hadron duality. Then we obtain the total widths Γ T Zcs = 15.31 ± 2.06 MeV and Γ M Zcs = 83.51 ± 21.09 MeV, which are consistent with the experimental data 13.8 +8.1 −5.2 ± 4.9 MeV from the BESIII collaboration and 131 ± 15 ± 26 MeV from the LHCb collaboration, respectively, and support assigning the Zcs(3985) and Zcs(4000) to be the hidden-charm tetraquark state and molecular state with the J P C = 1 +− , respectively.

The strange cousin of the $Z_c(4020/4025)$ as tetraquark state

“…we expect that the Z c (4020/4025) also have strange cousins Z cs , and they have analogous decay modes, the Z cs states may be observed in the decays to the final states D * D * s , D * s D * , h c K, etc. In this work, we tentatively assign the Z c (4020/4025) as the A Ā-type hidden-charm tetraquark state with the J P C = 1 +− , and extend our previous work to study the mass and width of its strange cousin with the QCD sum rules [20,23,27,28], the predictions can be confronted to the experimental data in the future. As a byproduct, we obtain the mass of the hidden-strange tetraquark state and the partial decay widths of the Z c (4020/4025).…”

“…The most significant state, Z + cs (4000), has the Breit-Wigner mass and width M = 4003 ± 6 +4 −14 MeV and Γ = 131 ± 15 ± 26 MeV, respectively, and the spin-parity J P = 1 + [18]. Although in both the pictures of the tetraquark state and molecular state, we can reproduce the mass of the Z cs (3985/4000) with the QCD sum rules [19,20,21,22,23,24,25,26], direct calculations of the decay widths based on the QCD sum rules support assigning the Z cs (3985) and Z cs (4000) to be the hidden-charm tetraquark state and molecular state with the J P C = 1 +− , respectively, or at least, the Z cs (3985) maybe have large diquark-antidiquark type Fock component, while the Z cs (4000) maybe have large color-singlet-color-singlet type Fock component [27].…”

“…According to the analysis in Refs. [27,37,38,39,40,41], we can introduce the parameters C hcK , C J/ψK and C ηcK * to parameterize the higher resonance and continuum states involving the Z cs channel,…”

“…We can see that the parameter C hcK is necessary, the parameters C J/ψK and C ηcK * are implied in the same way. We accomplish the operator product expansion up to the vacuum condensates of dimension 5 and neglect the tiny gluon condensate contributions [27,37,38,39,40,41], then obtain the QCD spectral densities ρ QCD (p ′2 , s, u) through double dispersion relation,…”

“…At the QCD side, we choose the flavor numbers n f = 4 and set the energy scale to be µ = 1.3 GeV, just like in previous work on the decays of the Z cs (3985/4000) [27]. At the hadron side, we take the parameters as M K = 0.4937 GeV, M π = 0.13957 GeV, M K * = 0.8917 GeV, M ρ = 0.77526 GeV, M J/ψ = 3.0969 GeV, M ηc = 2.9834 GeV, M hc = 3.525 GeV [4], f K = 0.156 GeV, f π = 0.130 GeV [4], f K * = 0.220 GeV, f ρ = 0.215 GeV, [43], f hc = 0.235 GeV, f J/ψ = 0.418 GeV, f ηc = 0.387 GeV [44], s 0 hc = 4.05 GeV, s 0 J/ψ = 3.6 GeV, s 0 ηc = 3.5 GeV [4],…”