Analysis of the tensor–tensor type scalar tetraquark states with QCD sum rules

The European Physical Journal C, Nov 2016

In this article, we study the ground states and the first radial excited states of the tensor–tensor type scalar hidden-charm tetraquark states with the QCD sum rules. We separate the ground state contributions from the first radial excited state contributions unambiguously, and obtain the QCD sum rules for the ground states and the first radial excited states, respectively. Then we search for the Borel parameters and continuum threshold parameters according to four criteria and obtain the masses of the tensor–tensor type scalar hidden-charm tetraquark states, which can be confronted with the experimental data in the future.

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Analysis of the tensor–tensor type scalar tetraquark states with QCD sum rules

Eur. Phys. J. C Analysis of the tensor-tensor type scalar tetraquark states with QCD sum rules Zhi-Gang Wang 0 Jun-Xia Zhang 0 0 Department of Physics, North China Electric Power University , Baoding 071003 , People's Republic of China In this article, we study the ground states and the first radial excited states of the tensor-tensor type scalar hidden-charm tetraquark states with the QCD sum rules. We separate the ground state contributions from the first radial excited state contributions unambiguously, and obtain the QCD sum rules for the ground states and the first radial excited states, respectively. Then we search for the Borel parameters and continuum threshold parameters according to four criteria and obtain the masses of the tensor-tensor type scalar hidden-charm tetraquark states, which can be confronted with the experimental data in the future. - The attractive interaction induced by one-gluon exchange favors formation of diquark states in color antitriplet and disfavors formation of diquark states in color sextet. The antitriplet diquark states εi jk q Tj C qk have five Dirac tensor structures, scalar C γ5, pseudoscalar C , vector C γμγ5, axial-vector C γμ and tensor C σμν . The structures C γμ and C σμν are symmetric, while the structures C γ5, C and C γμγ5 are antisymmetric. The scalar and axial-vector light diquark states have been studied with the QCD sum rules [1–4], the scalar and axial-vector heavy-light diquark states have also been studied with the QCD sum rules [5,6]. The calculations based on the QCD sum rules indicate that the scalar and axialvector diquark states are more stable than the corresponding pseudoscalar and vector diquark states, respectively. We usually construct the C γ5 ⊗ γ5C -type and C γμ ⊗ γ μC type currents to study the lowest scalar light tetraquark states, hidden-charm or hidden-bottom tetraquark states [7– 18], the corresponding C ⊗ C -type and C γμγ5 ⊗ γ5γ μC type scalar tetraquark states have much larger masses. The C σαβ ⊗ σ αβ C -type scalar hidden-charm or hidden-bottom tetraquark states have not been studied with the QCD sum rules, so it is interesting to study them with the QCD sum rules. The instantons play an important role in understanding the UA(1) anomaly and in generating the spectrum of light hadrons [19]. The calculations based on the random instanton liquid model indicate that the most strongly correlated diquarks exist in the scalar and tensor channels [20]. The heavy-light tensor diquark states, although they differ from the light tensor diquark states due to the appearance of the heavy quarks, maybe play an important role in understanding the rich exotic hadron states, we should explore this possibility, the lowest hidden-charm and hidden-bottom tetraquark states maybe of the C γ5 ⊗ γ5C -type, C γμ ⊗ γ μC -type or C σαβ ⊗ σ αβ C -type. The QCD sum rules method provides a powerful theoretical tool in studying the hadronic properties, and it has been applied extensively to the study of the masses, decay constants, hadronic form-factors, coupling constants, etc. [21– 23]. In this article, we construct the C σαβ ⊗ σ αβ C -type currents to study the scalar hidden-charm tetraquark states. There exist some candidates for the scalar hidden-charm tetraquark states. In Ref. [24], Lebed and Polosa propose that the X (3915) is the ground state scalar csc¯s¯ state based on lacking of the observed D D¯ and D∗ D¯ ∗ decays, and attribute the single known decay mode J /ψ ω to the ω–φ mixing effect. Recently, the LHCb collaboration observed two new particles X (4500) and X (4700) in the J /ψ φ mass spectrum with statistical significances 6.1σ and 5.6σ , respectively, and determined the quantum numbers to be J PC = 0++ with statistical significances 4.0σ and 4.5σ , respectively [25,26]. The X (4500) and X (4700) are excellent candidates for the csc¯s¯ tetraquark states. In Refs. [27,28], we study the C γμ ⊗ γ μC -type, C γμγ5 ⊗ γ5γ μC -type, C γ5 ⊗ γ5C type, and C ⊗ C -type scalar csc¯s¯ tetraquark states with the QCD sum rules. The numerical results support assigning the X (3915) to be the 1S C γ5 ⊗ γ5C -type or C γμ ⊗ γ μC type csc¯s¯ tetraquark state, assigning the X (4500) to be the 2S C γμ ⊗ γ μC -type csc¯s¯ tetraquark state, assigning the × Tr σ αβ C n n(−x )σ μν C Sm mT (−x )C , d¯u ( p) = i εi jk εimnεi j k εi m n where Si j (x ), Ui j (x ), Di j (x ) and Ci j (x ) are the full s, u, d and c quark propagators, respectively, i δi j x δi j ms Si j (x ) = 2π 2x 4 − 4π 2x 2 − X (4700) to be the 1S C γμγ5 ⊗ γ5γ μC -type csc¯s¯ tetraquark state. For other possible assignments of the X (4500) and X (4700), one can consult Refs. [29–34]. In this article, we study the C σαβ ⊗ σ αβ C -type hidden-charm tetraquark states with the QCD sum rules, and explore whether or not the X (3915), X (4500) and X (4700) can be assigned to be the C σαβ ⊗ σ αβ C -type tetraquark states. The article is arranged as follows: we derive the QCD sum rules for the masses and p (...truncated)


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Zhi-Gang Wang, Jun-Xia Zhang. Analysis of the tensor–tensor type scalar tetraquark states with QCD sum rules, The European Physical Journal C, 2016, pp. 650, Volume 76, Issue 12, DOI: 10.1140/epjc/s10052-016-4514-x