Tetraquark state candidates: Y(4260), Y(4360), Y(4660), and $$Z_c(4020/4025)$$ Z c ( 4020 / 4025 )

Zhi-Gang Wang

doi:10.1140/epjc/s10052-016-4238-y

Abstract

In this article, we construct the axialvector-diquark-axialvector-antidiquark type tensor current to interpolate both the vector and axialvector tetraquark states, then calculate the contributions of the vacuum condensates up to dimension-10 in the operator product expansion, and obtain the QCD sum rules for both the vector and axialvector tetraquark states. The numerical results support assigning the $Z_c(4020/4025)$ to be the $J^{PC}=1^{+-}$ diquark-antidiquark type tetraquark state, and assigning the $Y(4660)$ to be the $J^{PC}=1^{--}$ diquark-antidiquark type tetraquark state. Furthermore, we take the $Y(4260)$ and $Y(4360)$ as the mixed charmonium-tetraquark states, and construct the two-quark-tetraquark type tensor currents to study the masses and pole residues. The numerical results support assigning the $Y(4260)$ and $Y(4360)$ to be the mixed charmonium-tetraquark states.

Highlights

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, the measured mass and width are 4259 ± 8+−26 MeV and 88 ± 23+−64 MeV, respectively [1]
In Ref. [26], Albuquerque and Nielsen take the Cγ5 ⊗ γ5γμC type current to study the Y (4660) with the QCD sum rules and obtain the value MY (4660) = 4.65 GeV, which is in excellent agreement with the mass of the Y (4660)
Ref. [27], we suggest the formula μ = MX2 /Y/Z − (2Mc)2 with the effective mass Mc to determine the energy scales of the QCD spectral densities of the hidden charmed tetraquark states, and we evolve the vacuum condensates and the M S mass to the energy scale μ using the C ⊗ γμC type current; we obtain the mass 4.66 or 4.70 GeV for the Y (4660)

Summary

Introduction

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, the measured mass and width are 4259 ± 8+−26 MeV and 88 ± 23+−64 MeV, respectively [1]. [26], Albuquerque and Nielsen take the Cγ5 ⊗ γ5γμC type current to study the Y (4660) with the QCD sum rules and obtain the value MY (4660) = 4.65 GeV, which is in excellent agreement with the mass of the Y (4660) [27], we suggest the formula μ = MX2 /Y/Z − (2Mc) with the effective mass Mc to determine the energy scales of the QCD spectral densities of the hidden charmed tetraquark states, and we evolve the vacuum condensates and the M S mass to the energy scale μ using the C ⊗ γμC type current; we obtain the mass 4.66 or 4.70 GeV for the Y (4660). Type tensor current without introducing the additional P-wave to interpolate both the vector- and the axialvector-tetraquark states, and study the Y (4260), Y (4360), Y (4660/4630), and Zc(4020/4025) with the QCD sum rules by calculating the operator product expansion up to the vacuum condensates of dimension 10. The vacuum condensates are vacuum expectations of the operators of the order O(αs) both in the terms

T2 compared with the operator in

Conclusion