Is Ds(2700) a charmed tetraquark state?

In this article, we assume that the D_s(2700) is a tetraquark state, which consists of a scalar diquark and a vector antidiquark, and calculate its mass with the QCD sum rules. The numerical result indicates that the mass of the vector charmed tetraquark state is about M_V=(3.75±0.18) GeV or M_V=(3.71±0.15) GeV from different sum rules, which is about 1 GeV larger than the experimental data. Such tetraquark omponent should be very small in the D_s(2700).     

Analysis of X（1576） as a Tetraquark State with the QCD Sum Rules

We take the viewpoint that X（1576） is the tetraquark state which consists of a scalar diquark and an antiscalar-diquark in relative P-wave, and calculate its mass in the framework of the QCD sum rule approach. The numerical value of the mass mx= （1.66 =k 0.14） GeV is consistent with the experimental data. There might be some tetraquark components in the vector meson X（1576）.     

A family of double-beauty tetraquarks: Axial-vector state ■

The spectroscopic parameters and decay channels of the axial-vector tetraquark ■(in what follows,■ are explored using the quantum chromodynamics(QCD) sum rule method.The mass and coupling of this state are calculated using two-point sum rules by taking into account various vacuum condensates,up to 10 dimensions.Our prediction for the mass of this state m=(10215±250) MeV confirms that it is stable with respect to strong and electromagnetic decays and can dissociate to conventional mesons only via weak transformations.We investigate the dominant semileptonic ■ and nonleptonic ■ decays of ■.In these processes,■ is a scalar tetraquark ■ built of a color-triplet diquark and an antidiquark,whereas M is one of the vector mesons ρ~-,K~*(892),D~*(2010)~-,and D_s~(*-).To calculate the partial widths of these decays,we use the QCD three-point sum rule approach and evaluate the weak transition form factors G_i(i=0,1,2,3),which govern these processes.The full width Γ_(full)=(12.9±2.1) × 10~(-8) MeV and the mean lifetime τ=5.1+_(-0.71) ~(+0.99) fs of the tetraquark ■ are computed using the aforementioned weak decays.The obtained information about the parameters of ■ and ■ is useful for experimental investigations of these double-heavy exotic mesons.     

Vector hidden-bottom tetraquark candidate: Y(10750)

In this article,we take the scalar diquark and antidiquark operators as the basic constituents,and construct the Cγ_5■γ_5C type tetraquark current to study Y(10750) with the QCD sum rules.The predicted mass M_Y=10.75±0.10 GeV and width Γ_Y=33.60_(-9.45)~(+16.64) MeV support the assignment of Y(10750) as the diquark-antidiquark type vector hidden-bottom tetraquark state,with a relative P-wave between the diquark and antidiquark constituents.     

Analysis of Y（4660） and Related Bound States with QCD Sum Rules

In this article, we take the vector charmonium-like state Y（4660） as a φ＇ fo（980） bound state （irrespective of the hadro-charmonium and the molecular state） tentatively, and study its mass using the QCD sum rules. The numerical value My = 4.71 ±0.26 GeV is consistent with the experimental data. Considering the SU（3） symmetry of the light flavor quarks and the heavy quark symmetry, we also study the bound states φ＇a（400-1200）, γ′″ fo（980）, and γ′″σ（400-1200） with the QCD sum rules, and make reasonable predictions for their masses.     

A family of double-beauty tetraquarks:Axial-vector state T^-bb;us^-

The spectroscopic parameters and decay channels of the axial-vector tetraquark Tho(in what follows,TAV)are explored using the quantum chromodynamics(QCD)sum rule method.The mass and coupling of this state are calculated using two-point sum rules by taking into account various vacuum condensates,up to 10 dimensions.Our prediction for the mass of this state m=(10215±250)MeV confirms that it is stable with respect to strong and electromagnetic decays and can dissociate to conventional mesons only via weak transformations.We investigate the dominant semileptonic■and nonleptonic T AV b:s^-→v10 b:s^-M decays of T AV b:s^-.In these processes,Z-b:s^-is a scalar tetraquark[be][us^-]built of a colo-triplet diquark and an antidiquark,whereas M is one of the vector mesonsρ^-,K^*(892),D^*(2010)^-,and D^*s-.To caleulate the partial w idths of these decays,we use the QCD three-point sum rule approach and evaluate the weak transition form factors Gi(i=0,1,2,3),which govem these processes.The full widthΓfull=(12.9±2.1)×10^-8 MeV and the mean lifetimeτ=5.1+0.99-0.71 fs of the tetraquark TAV are computed us-ing the aforementioned weak decays.The obtained information about the parametersof TAY and Zh,is useful for experimental investigations of these double-heavy exotic mesons.     

Ds（0^±） Meson Spectroscopy in Gaussian Sum Rules

Masses of the Ds（0^±） mesons are investigated from a view-point of ordinary light-heavy system in the framework of the Gaussian sum rules, which are worked out by means of the Laplacian transformation to the usual Borel sum rules. Using the standard input of QCD non-perturbative parameters, the corresponding mass spectra and couplings of the currents to the Ds（0^±） mesons are obtained. Our results are mDs（0-） = 1.968±0.016±0.003 GeV and mDs（0＋） = 2.320 ±0.014 ± 0.003 GeV, which are in good accordance with the experimental data, 1.969 GeV and 2.317 GeV.     

QCD Sum Rules Study of X（4350）

The QCD sum rule approach is used to analyze the nature of the recently observed new resonance X （4350）, which is assumed to be a diquark-antidiquark state [cs][cs] with jPC = 1-＋. The interpolating current representing this state is proposed. In the calculation, contributions of operators up to dimension six are included in the operator product expansion （OPE）, as well as terms which are linear in the strange quark mass ms. We find ml-＋ = （4.82 ~ 0.19） GeV, which is not compatible with the X（4350） structure as a 1-＋ tetraquark state. Finally, we also discuss the difference of a four-quark state＇s mass whether the state＇s interpolating current has a definite charge conjugation.     

Mixed Quark-Gluon Condensate Beyond Chiral Limit

Using the Dyson-Schwinger equation and perturbation theory, we calculate the mixed quark-gluon condensates in the chiral limit and in the case of nonzero quark current mass for the light quark u/d and strange quark s. The results show that the mixed quark-gluon condensate will decrease when the quark mass increases. For the quark with zero mass, we obtain mo2 = g（qσuvGuvq）/（qq） 0.68 GeV2, which is in good agreement with the QCD sum rules estimate mo2=（0.8± 0.2） GeV2.     

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 mass M_Z=3.99±0.09 GeV is in excellent agreement with the experimental value 3985.2_(-2.0)~(+2.1)±1.7 MeV from the BESⅢ collaboration,which supports identifying Z_(cs)(3985) as the cousin of Zc(3900) with quantum numbers J~(PC)=1~(+-).We take into account the light flavor S U(3) mass-breaking effect to estimate the mass spectrum of the diquark-antidiquark type hidden-charm tetraquark states with strangeness according to previous studies.     

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.     

Exotic vector charmonium and its leptonic decay width

We propose a novel type of interpolating field operator,which manifests the hybrid-like configuration that the charm quark-antiquark pair recoils against gluonic degrees of freedom.A heavy vector charmonium-like state with a mass of 4.33(2) GeV is disentangled from the conventional charmonium states in the quenched approximation.This state has affinity for the hybrid-like operators but couples less to the relevant quark bilinear operator.We also try to extract its leptonic decay constant and give a tentative upper limit that it is less than one tenth of that of J/ψ,which corresponds to a leptonic decay width about dozens of eV.The connection of this state with X(4260) is also discussed.     

Properties of the P_c(4312) pentaquark and its bottom partner

We present an analysis of the newly observed pentaquark P_c(4312)~+ to shed light on its quantum numbers.To do that,the QCD sum rules approach is used.The measured mass of this particle is close to the ∑_c~(++)D~-threshold and has a small width,which supports the possibility of its being a molecular state.We consider an interpolating current in a molecular form and analyze both the positive and negative parity states with spin-1/2.We also consider the bottom counterpart of the state with similar molecular form.Our mass result for the charm pentaquark state supports that the quantum numbers of the observed state are consistent with J~P=1/2~-.     

Possible JPC=0+- exotic states

We study possible exotic J^PC=0⁺- states using tetraquark interpolating currents with the QCD sum rule approach. The extracted masses are around 4.85GeV for the charmonium-like states and 11.25 GeV for the bottomonium-like states. There is no working region for the light tetraquark currents, which implies that the light 0⁺- state may not exist below 2GeV.     

Dynamical study of light scalar mesons below 1 GeV in a flux-tube model

The light scalar mesons below 1GeV configured as tetraquark systems are studied in the framework of the flux-tube model. Comparative studies indicate that a multi-body confinement,instead of the additive two-body confinement, should be used in a multiquark system.The σ and κ mesons could be well accommodated in the diquark-antidiquark tetraquark picture, and could be colour-confinement resonances. The a0(980) and fo(980) mesons are not described as KK molecular states and ns diquark-antidiquark states.However, the mass of the first radial excited state of the diquark-antidiquark state, nn is 1019 MeV,is close to the experimental data of the fo (980).     

Revisiting 1-＋ Light Hybrid from Monte-Carlo Based QCD Sum Rules

We reanalyze the 1 ＋ light hybrid from QCD sum rules with a Monte-Carlo based on uncertainty analysis. With 30% uncertainties in the accepted central values for QCD condensates and other input parameters, we obtain a prediction on the 1-＋ hybrid mass of 1.71 ± 0.22 GeV, which covers the mass of 7rl （1600）. We also study the correlations between the input and output parameters of QCD sum rules.     

Light four-quark states and QCD sum rule

The relations among four-quark states, diquarks and QCD sum rules are discussed. The situation of the existing, but incomplete studies of four-quark states with QCD sum rules is analyzed. Masses of some diquark clusters were attempted to be determined by QCD sum rules, and masses of some light tetraquark states were obtained in terms of the diquarks.     

D and Ds in mass loaded flux tube

Heavy-light hadrons are studied in a mass loaded flux tube model. The study indicates that the dynamics of mesons and baryons containing a c quark is described well by the mass loaded flux tube. The hypothesis of good diquark-antiquark degeneracy is found reasonable in heavy-light quark systems. The spectrum of charmed （D） and charmed strange （Ds） mesons is systematically computed. D and Ds in 1D multiplets are predicted to have lower masses in comparison with other theoretical predictions. The predicted masses of the 1（13D1） and the 3（13D3） Ds agree well with those of recently observed Ds1（2700）± and DsJ（2860）, respectively.     

Study of X(5568) in a unitary coupled-channel approximation of BK and B_sπ

The potential of the B meson and the pseudoscalar meson is constructed up to the next-to-leading order Lagrangian, and then the BK and B_sπ interaction is studied in the unitary coupled-channel approximation. A resonant state with a mass about 5568 MeV and J~P= 0~+is generated dynamically, which can be associated with the X(5568) state announced by the D0 Collaboration recently. The mass and the decay width of this resonant state depend on the regularization scale in the dimensional regularization scheme, or the maximum momentum in the momentum cutoff regularization scheme. The scattering amplitude of the vector B meson and the pseudoscalar meson is calculated, and an axial-vector state with a mass near 5620 MeV and J~P= 1~+is produced. Their partners in the charm sector are also discussed.     

Chiral SU（3） Quark Model Study of Tetraquark States： cnn^-s^-/css^-s^-

The new members of the charm-strange family Dsj^＊（2317）, Dsj（2460）, and Ds（2632）, which have the surprising properties, are challenging the present models. Many theoretical interpretations have been devoted to this issue. Most authors suggest that they are not the conventional cs^- quark model states, but possibly are four-quark states, molecule states, or mixtures of a P-wave cs^- and a four-quark state. In this work, we follow the four-quark-state picture, and study the masses of cnn^-s^-/css^-s^- states （n is u or d quark） in the chiral SU（3） quark model. The numerical results show that the mass of the mixed four-quark state （cnn^-s^-/css^-s^-） with spin parity j^P ： 0^＋ might not be Ds （2632）. At the same time, we also conclude that Dsj^＊（2317） and Dsj（2460） cannot be explained as the pure four-quark state.