Analysis of the Axialvector Doubly Heavy Tetraquark States with QCD Sum Rules

Abstract

In this article, we construct the diquark-antidiquark type current operators to study the axialvector Bc-like tetraquark states with the QCD sum rules. In calculations, we take the energy scale formula as a powerful constraint to choose the ideal energy scales of the QCD spectral densities and add detailed discussions to illustrate why we take the energy scale formula to improve the QCD sum rules for the doubly heavy tetraquark states. The predicted masses M Zb c (1 +− ) = 7.30 ± 0.08 GeV and M Zb c (1 ++ ) = 7.31 ± 0.08 GeV lie between the conventional 2P and 3P Bc states with J P = 1 + from the potential quark models, which is a typical feature of the diquark-antidiquark type Bc-like tetraquark states.

Lattice QCD investigation of a doubly-bottom b¯b¯ud tetraquark with quantum numbers ILeskovec1, Meinel2, Pflaumer3 et al. 2019Phys. Rev. D

“…(24), and we determine the corresponding k n cot δ 0 (k n ) using Eq. (26). We parametrize the scattering amplitude using the effective-range expansion (ERE),…”

All-heavy tetraquarks

“…Furthermore, it will be very easy to distinguish the all-heavy tetraquark states from the states which have been observed because their masses should be far away from the mass regions of the observed states. Thus, besides some previous works on the heavy tetraquark states [12][13][14][15][16][17], many new studies have been carried out in recent years [11,[18][19][20][21][22][23][24][25][26][27][28][29][30], although some of the conclusions are quite different from each other. In some works, it is predicted that there exist stable bound tetraquark cccc states and/or bound tetraquark bbbb states with relatively smaller masses below the thresholds of heavy charmonium pairs [11,[21][22][23][24][25][26][27][28].…”

Analysis of the triply-charmed pentaquark states with QCD sum rules

“…as a powerful constraint to satisfy. In previous works, we observed that the energy scale formula can enhance the pole contribution remarkably for the tetraquark (molecular) states and pentaquark (molecular) states [13,14,23,28,29]. Now let us optimize the continuum threshold parameter s 0 and choose the best Borel parameter T 2 via trial and error, and finally obtain the Borel window, the continuum threshold parameter, the best energy scale of the QCD spectral density, and the pole contribution, which are shown in Table 1.…”

“…In the QCD sum rules for the tetraquark (molecular) states, pentaquark (molecular) states and hexaquark states (or dibaryon states), we take into the vacuum condensates, which are vacuum expectations of the quark-gluon operators of the order O(α k s ) with k ≤ 1 in a consistent way [12,13,14,23,24,25,28,29]. In the present case, if take the truncation k ≤ 1, the highest dimensional vacuum condensates are qq 3 αsGG π and qq qg s σGq 2 , the vacuum condensates αsGG π qq 2 qg s σGq , g 3 s GGG qq 3 and qg s σGq 3 come from the quark-gluon operators of the order O(α 3 2 s ) and should be discarded.…”

“…The observation of the Ξ ++ cc provides valuable experimental information on the strong correlation between the two charm quarks, which maybe shed light on the spectroscopy of the doubly-charmed baryon states, tetraquark states, pentaquark states and hexaquark states. For the heavy-quark-heavy-quark systems QQ, only the axialvector diquark operators ε ijk Q T j Cγ µ Q k and tensor diquark operators ε ijk Q T j Cσ µν Q k can exist due to the Fermi-Dirac statistics, we usually take the axialvector diquark operators ε ijk Q T j Cγ µ Q k as the basic constituents to construct the four-quark currents to study the doubly heavy tetraquark states with the QCD sum rules [20,21,22,23]. For the doubly heavy hexaquark states, we can choose the doubly heavy diquark operators ε ijk Q T j Cγ µ Q k or heavy diquark operators ε ijk q T j Cγ 5 Q k and ε ijk q T j Cγ µ Q k as the basic constituents to construct the six-quark currents.…”