Analysis of Scalar Doubly Heavy Tetraquark States with QCD Sum Rules

In this article, we perform a detailed study of the mass spectrum of the scalar doubly charmed and doubly bottom tetraquark states using the QCD sum rules.

Fully-light vector tetraquark states with explicit P-wave via QCD sum rules

In this study,we apply the QCD sum rules to investigate the vector fully-light tetraquark states with an explicit P-wave between the diquark and antidiquark pairs.We observed that the Cγα⊗↔∂μ⊗γαC(or Cγα⊗↔Dμ⊗γαC)type current with fully-strange quarks couples potentially to a tetraquark state with a mass 2.16±0.14GeV,which supports assigning Y(2175)/ϕ(2170)as the diquark-antidiquark type tetraquark state with JPC=1−−.The qsˉqˉs and ssˉsˉs vector tetraquark states with the structure Cγμ⊗↔∂α⊗γαC+Cγα⊗↔∂α⊗γμ(or Cγμ⊗↔Dα⊗γαC+Cγα⊗↔Dα⊗γμ)are consistent with X(2200)and X(2400),respectively,which lie in the region from 2.20 to 2.40GeV.The central values of the masses of the fully-strange vector tetraquark states with an explicit P-wave are approximately 2.16−3.13GeV(or 2.16−3.16GeV).Predictions for other fully-light vector tetraquark states with and without hidden-strange are also presented.

D-wave excited cscs tetraquark states with J^(PC)=1^(++)and 1^(+-)

We study the mass spectra of D-wave excited cscs tetraquark states with J^(PC)=1^(++)and 1^(+-)in both symmetric 6cs@6cs and antisymmetric 3cs@3cs color configurations using the QCD sum rule method.We construct the D-wave diquark-antidiquark type of cscs tetraquark interpolating currents in various excitation structures with(L_(λ),Lp{p_(1),p_(2)})=(2,0(0,0),(1,1(1,0),(1,1(0,1),(0,2(1,1),(0,2(2,0),(0,2(0,2).Our results support the interpretation of the recently observed X(4685)resonance as a D-wave cscs tetraquark state with JPC-1++in the(2,O(0,O))or(0,2(2,O))excitation mode,although some other possible excitation structures cannot be excluded exhaustively within theoretical errors.Moreover,our results provide the mass relations 6_(ρρ)<3_(λλ)<3_(λρ)<3_(ρρ)and 6pp<3au<6aa<3pp for the positive and negative C-parity D-wave cscs tetraquarks,respectively.We suggest searching for these possible D-wave cscs tetraquarks in both the hidden-charm channels J/o and nc,as well as open-cham channes such as D_(s)D_(x)nd D_(s)D_(s1).

Investigation of the tetraquark states QqQq in the improved chromomagnetic interaction model

In the framework of the improved chromomagnetic interaction model,we complete a systematic study of the S-wave tetraquark states QqQq(Q=c,b,and q=u,d,s)with different quantum numbers:J^(PC)=0^(+(+)),1^(+(±)),and 2^(+(+)).The mass spectra of tetraquark states are predicted,and the possible decay channels are analyzed by considering both the angular momentum and C-parity conservation.The recently observed hidden-charm tetraquark states with strangeness,such as Z_(cs)(3985)^(-),X(3960),and Z_(cs)(4220)^(+),can be well explained in our model.Additionally,according to the wave function of each tetraquark state,we find that the low-lying states of each QqQq configuration have a large overlap to the QQ and qq meson basis,instead of the Qq and qQ meson basis.This indicates that one can search these tetraquark states in future experiments via the channel of QQ and qq mesons.

Scalar Hidden-Charm Tetraquark States with QCD Sum Rules

In this article, we study the masses and pole residues of the pseudoscalar-diquark-pseudoscalar-antidiquark type and vector-diquark-vector-antidiquark type scalar hidden-charm cucd （cucs） tetraquark states with QCD sum rules by taking into account the contributions of the vacuum condensates up to dimension-lO in the operator product expansion. The predicted masses can be confronted with the experimental data in the future. Possible decays of those tetraquark states are also discussed.

Reanalysis of the Z_c(4020), Z_c(4025), Z(4050) and Z(4250) as Tetraquark States with QCD Sum Rules

In this article, we calculate the contributions of the vacuum condensates up to dimension-10 in the operator product expansion, and study the C γμ- Cγνtype scalar, axial-vector and tensor tetraquark states in details with the QCD sum rules. In calculations, we use the formula μ = √M^2X/ Y /Z-（2Mc）^2 to determine the energy scales of the QCD spectral densities. The predictions MJ =2=（4.02-0.09^＋0.09） GeV, MJ =1=（4.02-0.08^＋0.07） GeV favor assigning the Zc（4020） and Zc（4025） as the J^PC= 1^＋-or 2^＋＋diquark-antidiquark type tetraquark states, while the prediction MJ =0=（3.85-0.09^＋0.15） GeV disfavors assigning the Z（4050） and Z（4250） as the J^P C= 0^＋＋ diquark-antidiquark type tetraquark states. Furthermore, we discuss the strong decays of the 0^＋＋, 1^＋-, 2^＋＋diquark-antidiquark type tetraquark states in details.

Magnetic and quadrupole moments of the Z_(c)(4020)^(+),Z_(c)(4050)^(+),and Z_(c)(4600)^(+)states in the diquark-antidiquark picture

The magnetic and quadrupole moments of the Z_(c)(4020)^(+),Z_(c)(4050)^(+),and Z_(c)(4600)^(+)states are calculated within the QCD light-cone sum rules.The compact diquark-antidiquark interpolating currents and the distribution amplitudes of the on-shell photon are used to extract the magnetic and quadrupole moments of these states.The magnetic moments are acquired asμZ_(c)=0.50+0.22−0.22μN,μZ_(c)^(1)=1.22+0.34−0.32μN,andμZ_(c)^(2)=2.40+0.53−0.48μN for the Z_(c)(4020)^(+),Z_(c)(4050)^(+),and Z_(c)(4600)^(+)states,respectively.The magnetic moments evaluated for the Z_(c)4020)+,Z_(c)(4050)+,and Z_(c)(4600)+states are sufficiently large to be experimentally measurable.The magnetic moment is an excellent platform for studying the internal structure of hadrons governed by the quark-gluon dynamics of QCD because it is the leading-order response of a bound system to a weak external magnetic field.The quadrupole moment results are DZ_(c)=(0.20+0.05−0.04)×10^(−3)fm^(2),DZ_(c)^(1)=(0.57+0.07−0.08)×10^(−3)fm^(2),and DZ_(c)^(2)=(0.30+0.05−0.04)×10^(−3)fm^(2)for the Z_(c)(4020)^(+),Z_(c)(4050)^(+),and Z_(c)(4600)^(+)states,respectively.We obtain a non-zero,but small,value for the quadrupole moments of the Z_(c)states,which indicates a non-spherical charge distribution.The nature and internal structure of these states can be elucidated by comparing future experimental data on the magnetic and quadrupole moments of the Z_(c)(4020)^(+),Z_(c)(4050)^(+),and Z_(c)(4600)^(+)states with the results of the present study.

Analysis of the tetraquark and hexaquark molecular states with the QCD sum rules

In this article,we construct the color-singlet-color-singlet type currents and the color-singlet-colorsinglet-color-singlet type currents to study the scalar D*■*,D*D*tetraquark molecular states and the vector D*D*■*,D*D*D*hexaquark molecular states with the QCD sum rules in details.In calculations,we choose the pertinent energy scales of the QCD spectral densities with the energy scale formula■for the tetraquark and hexaquark molecular states respectively in a consistent way.We obtain stable QCD sum rules for the scalar D*■*,D*D*tetraquark molecular states and the vector D*D*■*hexaquark molecular state,but cannot obtain stable QCD sum rules for the vector D*D*D*hexaquark molecular state.The connected(nonfactorizable)Feynman diagrams at the tree level(or the lowest order)and their induced diagrams via substituting the quark lines make positive contributions for the scalar D*D*tetraquark molecular state,but make negative or destructive contributions for the vector D*D*D*hexaquark molecular state.It is of no use or meaningless to distinguish the factorizable and nonfactorizable properties of the Feynman diagrams in the color space in the operator product expansion so as to interpret them in terms of the hadronic observables,we can only obtain information about the short-distance and long-distance contributions.

Analysis of X(5568) as Scalar Tetraquark State in Diquark-Antidiquark Model with QCD Sum Rules

In this article, we take the X(5568) as the diquark-antidiquark type tetraquark state with the spin-parity J^P= 0^+, construct the scalar-diquark-scalar-antidiquark type current, carry out the operator product expansion up to the vacuum condensates of dimension-10, and study the mass and pole residue in details with the QCD sum rules. We obtain the value M_X =(5.57 ± 0.12) Ge V, which is consistent with the experimental data. The present prediction favors assigning the X(5568) to be the scalar tetraquark state.

Tetraquark candidates in LHCb's di-J/ψ mass spectrum

In this article,we study the first radial excited states of the scalar,axialvector,vector,and tensor diquark-antidiquark-type cccc tetraquark states with the QCD sum rules and obtain the masses and pole residues;then,we use the Regge trajectories to obtain the masses of the second radial excited states.The predicted masses support assigning the broad structure from 6.2 to 6.8 GeV in the di-J/ψ mass spectrum to be the first radial excited state of the scalar,axialvector,vector,or tensor cccc tetraquark state,as well as assigning the narrow structure at about 6.9 GeV in the di-J/ψ mass spectrum to be the second radial excited state of the scalar or axialvector cccc tetraquark state.

Analysis of Z_(cs)(3985)as the axialvector tetraquark state

In this study,we choose the scalar and axialvector diquark operators in the color antitriplet as the fundamental building blocks to construct four-quark currents and investigate the diquark-antidiquark type axialvector tetraquark states ccus in the framework of the QCD sum rules.The predicted tetraquark massM_(Z)=3.99±0.09GeV is in excellent agreement with the experimental value 3985.2^(+2.1)_(-2.0)±1.7 MeV from the BESⅢ collaboration,which supports identifying Z_{cs}(3985) as the cousin of Z_(c)(3900) with quantum numbers J^(PC)=1^(+-).We take into account the light flavor SU(3) mass-breaking effect to estimate the mass spectrum of the diquark-antidiquark type hidden-charm tetraquark states with strangeness according to previous studies.

Strange cousin of Z_(c) (4020/4025) as a tetraquark state

Motivated by the analogous properties of Z_(c)(3900/3885)and Z_(cs)(3985/4000).we tentatively assign Z_(c)(4020=4025)as the AA^(-)-type hidden-charm tetraquark state with J^(PC)=1^(+-),where A denotes the axialvector diquark states,and explore AA^(-)-type tetraquark states without strange,with strange,and with hidden-strange via QCD sum rules in a consistent manner.We then explore the hadronic coupling constants in the two-body strong decays of tetraquark states without and with strange via QCD sum rules based on rigorous quark-hadron duality and acquire partial and total decay widths.The present calculations support assigning Z_(c)(4020=4025)as theAA^(-)-type tetraquark state with J^(PC)=1^(+-),while the predictions for its strange cousin Z_(cs)state can be confronted with experimental data in the future.

Axialvector tetraquark candidates for Zc(3900), Zc(4020),Zc(4430), and Zc(4600)

We construct the axialvector and tensor current operators to systematically investigate the ground and first radially excited tetraquark states with quantum numbers J^PC= 1^+-using the QCD sum rules. We observe one axialvector tetraquark candidate for Zc(3900) and Zc(4430), two axialvector tetraquark candidates for the Zc(4020), and three axialvector tetraquark candidates for Zc(4600).

Production of X_(eses)in heavy ion collisions

The yields of X_(cscs)with its two possible configurations,i.e.,the hadronic molecular state and tetraquark state,for Pb-Pb collisions at√sNN=5.02 TeV is studied.A volume effect is found from the centrality distribution of X_(cscs),which could help to distinguish the inner structure of X_(cscs).We also show the rapidity and the transverse momentum distributions of X_(cscs) production as well as its elliptic flow coefficient as a function of the transverse momentum.

Decay properties of the X(3872)through the Fierz rearrangement

We systematically construct all the tetraquark currents of J^(PC)=1^(++) with the quark configurations[cq][cq],[cq][qc],and[cc][qq](q=u/d).Their relations are derived using the Fierz rearrangement of the Dirac and color indices,through which we study decay properties of the X(3872)under both the compact tetraquark and hadronic molecule interpretations.We conduct a search for the X(3872)→χ_(c0)π,η_(c)ππ,and χ_(c1)ππ decay processes in particle experiments.

Analysis of the Z(4430) as the First Radial Excitation of the Z_c(3900)

In this article,we take the Zc(3900) and Z(4430) as the ground state and the first radial excited state of the axial-vector tetraquark states with J^(PC) = 1^(+-),respectively,and study their masses and pole residues with the QCD sum rules by calculating the contributions of the vacuum condensates up to dimension-10 in a consistent way in the operator product expansion.The numerical result favors assigning the Z_c(3900) and Z(4430) as the ground state and first radial excited state of the axial-vector tetraquark states,respectively.

Decay widths of Z_(cs)(3985/4000)based on rigorous quark-hadron duality

In this study,we explore the hadronic coupling constants G_(ZJ/ψK),G_(Zη_(c))K^(*),and G_(ZD*D_(s)) of the exotic states Z_(cs)(3985/4000)within the pictures of both the tetraquark and molecular states with the tentative assignments J^(PC)=1^(+-)based on rigorous quark-hadron duality.Subsequently,we obtain the total widthsΓ_(Z_(cs))^(T)=15.31±2.06 MeV and Γ_(Z_(cs))^(M)=83.51±21.09 Mev,which are consistent with experimental values from the BESⅢ collaboration,13.8_(-5.2)^(+8.1)±4.9 MeV,and LHCb collaboration,131±15±26 MeV,respectively,and support assigning Z_(cs)(3985)and Z_(cs)(4000)as the hidden-charm tetraquark and molecular states with J^(PC)=1^(+-),respectively.