Abstract
In this article, we take the pseudoscalar, scalar, axialvector, vector, tensor (anti)diquark operators as the basic constituents, and construct the scalar, axialvector and tensor tetraquark currents to study the mass spectrum of the ground state hidden-charm tetraquark states with the QCD sum rules in a comprehensive way. We revisit the assignments of the $X$, $Y$, $Z$ states, such as the $X(3860)$, $X(3872)$, $X(3915)$, $X(3940)$, $X(4160)$, $Z_c(3900)$, $Z_c(4020)$, $Z_c(4050)$, $Z_c(4055)$, $Z_c(4100)$, $Z_c(4200)$, $Z_c(4250)$, $Z_c(4430)$, $Z_c(4600)$, etc in the scenario of tetraquark states in a consistent way based on the QCD sum rules. Furthermore, we discuss the feasibility of applying the QCD sum rules to study the tetraquark states and tetraquark molecular states (more precisely, the color-singlet-color-singlet type tetraquark states), which begin to receive contributions at the order $\mathcal{O}(\alpha_s^0)$, not at the order $\mathcal{O}(\alpha_s^2)$.
Highlights
In 2003, the Belle Collaboration observed a narrow charmoniumlike state Xð3872Þ in the π þ π − J=ψ mass spectrum in the exclusive decays B → K π þ π − J=ψ [1], which cannot be accommodated in the conventional two quark model as the χ 0c1 state with the quantum numbersJPC 1⁄4 1þþ
Thereafter, about twenty charmoniumlike states were observed by the BABAR, Belle, BESIII, CDF, CMS, D0, LHCb Collaborations [2], which cannot be accommodated in the conventional two quark model and are denoted as the X, Y, and Z states ; some are still needing confirmation, and the quantum numbers have not been established yet
Ref. [21], we introduce a relative P wave between the diquark and antidiquark operators explicitly for constructing the tetraquark currents to systematically study the vector tetraquark states with the QCD sum rules and obtain the lowest vector tetraquark masses up to now, which support assigning the Yð4220=4260Þ, Yð4320=4360Þ, Yð4390Þ, and Zc ð4250Þ to be the vector hidden-charm tetraquark states
Summary
In 2003, the Belle Collaboration observed a narrow charmoniumlike state Xð3872Þ in the π þ π − J=ψ mass spectrum in the exclusive decays B → K π þ π − J=ψ [1], which cannot be accommodated in the conventional two quark model as the χ 0c1 state with the quantum numbers. The tensor diquark states have both J P 1⁄4 1þ and 1− components; we project out the 1þ and 1− components explicitly and denote the corresponding axialvector and vector diquarks as à and Ṽ, respectively All in all, those X, Y, and Z states have been studied with the QCD sum rules in one way or another [10,16,17,18,19,20,21,22,23,24,25,26,27, 29,30,31]; in the present work, we take the scalar, pseudoscalar, axialvector, vector, and tensor diquark operators as the basic building blocks to construct twenty tetraquark currents and study the mass spectrum of the hidden-charm tetraquark states with the QCD sum rules in a comprehensive way and revisit the assignments of the X and Z states in the scenario of tetraquark states and try to accommodate the exotic states as many as possible in a consistent way.
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