Abstract
In this article, we construct the C otimes gamma _mu C and Cgamma _5 otimes gamma _5gamma _mu C type currents to interpolate the vector tetraquark states, then carry out the operator product expansion up to the vacuum condensates of dimension-10 in a consistent way, and obtain four QCD sum rules. In calculations, we use the formula mu =sqrt{M^2_{Y}-(2{mathbb {M}}_c)^2} to determine the optimal energy scales of the QCD spectral densities, moreover, we take the experimental values of the masses of the Y(4260 / 4220), Y(4360 / 4320), Y(4390) and Y(4660 / 4630) as input parameters and fit the pole residues to reproduce the correlation functions at the QCD side. The numerical results support assigning the Y(4660 / 4630) to be the C otimes gamma _mu C type vector tetraquark state cbar{c}sbar{s}, assigning the Y(4360 / 4320) to be Cgamma _5 otimes gamma _5gamma _mu C type vector tetraquark state cbar{c}qbar{q}, and disfavor assigning the Y(4260 / 4220) and Y(4390) to be the pure vector tetraquark states.
Highlights
In Refs. [23,60,63,64], we study the energy scale dependence of the QCD sum rules in details and suggest an energy scale formula μ = MX2 /Y/Z − (2MQ)2 with the effective heavy quark mass MQ to determine the energy scales of the QCD spectral densities of the hidden-charm and hiddenbottom tetraquark states, which works well for the hidden-charm pentaquark states [72,73]
[36], we study the vector molecular states D D 1(2420) and sum r ules by taking into account the vacuum condensates up to dimension-10 in the operator product expansion in a consistent way, and use the energy scale formula for the molecular states to determine the optimal energy scales of the QCD spectral densities [74,75], and obtain the predications MDD 1(1−−) = 4.36 ± 0.08 GeV and
T2 c In Table 4, we present the central values of the fitted pole residues
Summary
In 2005, the BaBar collaboration studied the initial-state radiation process e+e− → γI SRπ +π − J/ψ and observed the Y (4260) in the π +π − J/ψ invariant-mass spectrum [1]. Belle collaboration studied the initial-state radiation process e+e− → γI SRπ +π −ψ , and observed two structures Y (4360) and Y (4660) in the π +π −ψ invariant-mass spectrum [9,10]. In the effective Hamiltonian, an approximately common rest frame for all the components is assumed, while in the dynamical diquark picture, the diquark–antidiquark pair forms promptly at the production point, and rapidly separates due to the kinematics of the production process, they create a color flux tube or string between them [17] Another possible assignment of the Y (4260) is the ccg hybrid state [25,26], the lattice calculations indicate that the vector charmonium hybrid has a mass about 4285 MeV, which is quite close to that of the Y (4260) [27]. Cγ5 ⊗ ∂μγ5C Cγ5 ⊗ γ5γμC C ⊗ γμC Cγμ ⊗ γν C − Cγν ⊗ γμC Cγ5 ⊗ γ5γμC Cγ5 ⊗ ∂μγ5C C ⊗ γμC ⊕ γμ C ⊗ γμC ⊕ γμ Cγ5 ⊗ γ5γμC ⊕ γμ Constituents ccssccssccss/ccqqccqqccqqccqqccqq ⊕ ccccqq ⊕ ccccqq ⊕ cc OPE (No)
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