Hidden-bottom and -charm hexaquark states in QCD sum rules

Abstract

In this paper, we investigate the spectra of the prospective hidden-bottom and -charm hexaquark states with quantum numbers J P C = 0 ++ , 0 −+ , 1 ++ and 1 −− in the framework of QCD sum rules.By constructing appropriate interpreting currents, the QCD sum rules analyses are performed up to dimension 12 of the condensates. Results indicate that there exist two possible baryonium states in b-quark sector with masses 11.84 ± 0.22 GeV and 11.72 ± 0.26 GeV for 0 ++ and 1 −− , respectively. The corresponding hidden-charm partners are found lying respectively at 5.19 ± 0.24 GeV and 4.78 ± 0.23GeV. Note that these baryonium states are all above the dibaryon thresholds, which enables their dominant decay modes could be measured at BESIII, BELLEII, and LHCb detectors. * wanbingdong16@mails.ucas.ac.cn † tangl@hebtu.edu.cn ‡ qiaocf@ucas.ac.cn, corresponding author Hadrons with more than the minimal quark content (qq or qqq) was proposed by Gell-Mann [1] and Zweig [2] in 1964, which were named as multiquark exotic states and do not infringe the Quantum Chromodynamics (QCD). Exploring the existence and properties of such exotic states is one of the most intriguing research topics of hadronic physics. In past few decades, research on the heavy-flavor exotic states has made tremendous developments, that is, many charmonium-like/bottomonium-like XYZ states have been observed [3-7]. In 2015, two hidden-charm pentaquarks P c (4380) and P c (4450) [8] were observed by the LHCb Collaboration in the J/ψ invariant mass spectrum via the Λ 0 b → J/ψpK − process. Recently, the LHCb Collaboration reported a new narrow state P c (4312), and the previously observed structure P c (4450) appears to be split into two narrower structures P c (4440) and P c (4457) [9].The recent experimental and theoretical progresses can be found in comprehensive reviews like [10][11][12][13][14].Facing the observations of tetraquark and pentaquark states, it is nature to conjecture that there should exist the hidden-charm and -bottom hexaquark states, and it is time to hunt for them. For the hexaquark states, the deuteron is a typical and well-established dibaryon molecular state with J P = 1 + and binding energy E B = 2.225MeV [15]. The baryonium states composed of a baryon and an anti-baryon is another special class of heaxquark configuration. In Refs. [16,17], the Λ c -Λ c structure was introduced to explain the production and decays of Y (4260). And the heavy baryonium was explored as well in the heavy baryon chiral perturbation theory [18,19].The method of QCD sum rules [20][21][22][23] has been applied successfully to many hadronic phenoemena, such as the hadron spectrum and hadron decays. In QCD sum rules, based on the proper interpreting currents corresponding to a hadron of interest, one can construct the two-point or three-point correlation functions, which are respectively used to evaluate the mass and the decay property of the related hadron. Then by matching its operator product expansion (OPE) to its hadronic saturation, the main function for ext...

Study of $Λ_c$$Λ_c$ dibaryon and $Λ_c$$\barΛ_c$ baryonium states via QCD sum rules

“…In contrary to the conclusion obtained in Ref. [11], we find the currents with the quantum numbers J P = 0 − and 1 + also exist Borel platforms. The vacuum condensates are calculated up to dimension 16, especially, for the current J 1 , we consider all the vacuum condensates up to dimension 16 and choose the truncation of the operator product expansion of the order O(α k s ) with k ≤ 3.…”

“…They are all above the thresholds of the two baryon constituents, which is qualitatively in agreement with the results obtained in Ref. [11]. In contrary to the conclusion obtained in Ref.…”

“…[10], the scalar and axialvector Ξ cc Σ c dibaryon states were studied using the color-singlet-color-singlet type interpolating currents. And very recently, the hidden-bottom and hidden-charm hexaquark molecular states with the quantum numbers J P C = 0 ++ , 0 −+ , 1 ++ , and 1 −− have been studied in the framework of the QCD sum rules [11]. It is proposed via the Bethe-Salpeter equation that the Λ c Λc baryonium states should contain at least two states: the Λ c Λc molecular state and another one with mass around 4.65GeV for the thresholds up to 4.7GeV [12].…”

Search for the charmed baryonium and dibaryon structures via the QCD sum rules

“…In recent years, several QCD-inspired models are applied to study the dibaryons and baryoniums, such as the quark delocalization color screening model [11,12], solving the Bethe-Salpeter equation via effective Lagrangians [13,14], constituent quark model [15,16], lattice QCD [17,18], the QCD sum rules [19][20][21][22][23][24] and so on. Especially, in Ref.…”

Light baryonium spectrum

“…Entering the new millennium, the heavy baryon-antibaryon hadronic structures, and hence the term of baryonium, were proposed and employed to explain the extraordinary nature of Y (4260) [15,16] and other charmonium-like states observed in experiments. Later on, more investigations on baryonium are performed from various aspects [17][18][19][20][21][22]. Partly due to the the small spacings between light hadron states, it is normally hard to discriminate exotic states from conventional ones.…”