Is J~(PC)=3~(-+) molecule possible?

The confirmation of charged charmonium-like states indicates that heavy quark molecules should exist.Here we discuss the possibility of a molecule state with J P C= 3-+. In a one-boson-exchange model investigation for the S wave C = + D* ˉD*2states, one finds that the strongest attraction is in the case J = 3 and I = 0 for bothπ and σ exchanges. Numerical analysis indicates that this hadronic bound state might exist if a phenomenological cutoff parameter around 2.3 Ge V(1.5 Ge V) is reasonable with a dipole(monopole) type form factor in the one-pionexchange model. The cutoff for binding solutions may be reduced to a smaller value once the σ exchange contribution is included. If a state around the D* ˉD*2threshold(≈4472 Me V) in the channel J/ψω(P wave) is observed, the heavy quark spin symmetry implies that it is not a cˉc meson and the J P C are likely to be 3-+.     

Calculation of the Mass of X（3872） by the Mandelstam Generalization of the Gell-Mann-Low Method

On the basis of assuming that the narrow state X（3872） is a molecule state consisting of D0 and D＊0, we apply the Mandelstam generalization of the Ge11-Mann-Low method to calculate the matrix element of quark current between the heavy meson states described by Bether-Salpeter wave function. In calculation of the matrix element of quark current the operator product expansion is used in order to include the nonperturbative contribution of the vacuum condensates. In this scheme we calculate the mass of X（3872）. We believe that this scheme is closer to QCD than the previous work.     

Energy loss of charm quarks from J/ψ production in cold nuclear matter

J/ψ suppression in p-A collisions is studied by considering the nuclear effects on parton distribution,energy loss of beam proton and the finial state energy loss of color octet cc. The leading-order computations for J/ψproduction cross-section ratios RW/Be(x F) are presented and compared with the selected E866 experimental data with the cc remaining colored on its entire path in the medium. It is shown that the combination of the different nuclear effects accounts quite well for the observed J/ψ suppression in the experimental data. It is found that the J/ψ suppression on RW/Be(x F) from the initial state nuclear effects is more important than that induced by the energy loss of color octet cc in the large x F region. Whether the cc pair energy loss is linear or quadratic with the path length is not determined. The obtained cc pair energy loss per unit path length α = 2.78±0.81 Ge V/fm, which indicates that the heavy quark in cold nuclear matter can lose more energy compared to the outgoing light quark.     

Spectrum for heavy quarkonia and mixture of the relevant wave functions within the framework of Bethe-Salpeter equation

Considering the fact that some excited states of the heavy quarkonia (charmonium and bottomonium) are still missing in experimental observations and potential applications of the relevant wave functions of the bound states,we re-analyze the spectrum and the relevant wave functions of the heavy quarkonia within the framework of Bethe-Salpeter (B.S.) equation with a proper QCDinspired kernel.Such a kernel for the heavy quarkonia,relating to potential of the non-relativistic quark model,is instantaneous,so we call the corresponding B.S.equation as BS-In equation throughout the paper.Particularly,a new way to solve the B.S.equation,which is different from the traditional ones,is proposed here,and with it not only the known spectrum for the heavy quarkonia is re-generated,but also an important issue is brought in,i.e.,the obtained solutions of the equation ‘automatically’ include the ‘fine’,‘hyperfine’ splittings and the wave function mixture,such as S-D wave mixing in J PC = 1-states,P-F wave mixing in J PC = 2 ++ states for charmonium,bottomonium etc.It is pointed out that the best place to test the wave mixture probably is at Z-factory (e + e-collider running at Z-boson pole with extremely high luminosity).     

Understanding the structure of d~*(2380) in chiral quark model

The structure and decay properties of d~* have been detailedly investigated in both the chiral SU(3) quark model and the extended chiral SU(3) quark model that describe the energies of baryon ground states and the nucleon-nucleon(NN) scattering data satisfactorily. By performing a dynamical coupled-channels study of the system of ?? and hidden-color channel(CC) with quantum numbers I(J~P) = 0(3~+) in the framework of the resonating group method(RGM), we find that the d~* has a mass of about 2.38-2.42 Ge V and a root-mean-square radius(RMS) of about 0.76-0.88 fm. The channel wave function is extracted by a projection of the RGM wave function onto the physical basis, and the fraction of CC component in the d~* is found to be about 66%-68%, which indicates that the d~* is a hexaquark-dominated exotic state. Based on this scenario the partial decay widths of d~*→dπ~0π~0and d~*→dπ~+π~- are further explicitly evaluated and the total width is then obtained by use of the branching ratios extracted from the measured cross sections of other possible decay channels. Both the mass and the decay width of d~* calculated in this work are compatible with the data(M≈2380 Me V, Γ≈70 Me V) reported by WASA-at-COSY Collaboration.     

QQqq Four-Quark Bound States in Chiral SU（3） Quark Model

Abstract The possibility of QQqq heavy-light four-quark bound states has been analyzed by means of the chiral SU（3） quark model, where Q is the heavy quark （c or b） and q is the light quark （u, d, or s）. We obtain a bound state for the bbnn configuration with quantum number JR=1^＋, I = 0 and for the ccnn （JR=1^＋, I=O） configuration, which is not bound but slightly above the D^＊ D^＊ threshold （n is u or d quark）. Meanwhile, we also conclude that a weakly bound state in bbnn system can also be found without considering the ehiral quark interactions between the two light quarks, yet its binding energy is weaker than that with the chiral quark interactions.     

Heavy Quarks Production in Hadronic Processes： Qualitative Study of Higher-Order Fock States

The contribution of the two particles Fock states for the production of a heavy quark in proton-pion and photon-pion collisions is studied. It is shown that the effect depends strongly on the produced heavy quark mass, and the choice of the factorization scale.     

Energy loss effect of incoming gluons from J/ψ production in p-A collisions

The energy loss effect of incoming gluons from J/ψ production in p-A(or d-A) collisions is investigated by means of the E866, RHIC and LHC experimental data. The gluon mean energy loss per unit path length d E/d L = 2.18 ± 0.14 Ge V/fm is extracted by fitting the E866 experimental data for J/ψ production cross section ratios R W(Fe)/Be(x F). The obtained result indicates that the incoming gluons lose more energy than the incident quarks. By comparing the theoretical results with E866, RHIC, and LHC experimental data, it is found that the nuclear suppression due to the incident gluon(quark) energy loss reduces(increases) with the increase of the kinematic variable x F(or y). The energy loss effect of incoming gluons plays an important role in the suppression of J/ψ production in a wide energy range from√s = 38.7 Ge V to√s = 5.0 Te V, and the influence of incident quark energy loss can be ignored for high energies(such as at RHIC and LHC energy).     

Is d* a candidate for a hexaquark-dominated exotic state?

We confirm our previous prediction of a d* state with I(JP) = 0(3+) [Phys. Rev. C 60, 045203(1999)] and report for the first time based on a microscopic calculation that d* has about 2/3 hidden color(CC)configurations and thus is a hexaquark-dominated exotic state. By performing a more elaborate dynamical coupledchannels investigation of the △△-CC system within the framework of the resonating group method(RGM) in a chiral quark model, we find that the d* state has a mass of about 2.38–2.42 Ge V, a root-mean-square radius(RMS) of0.76–0.88 fm, and a CC fraction of 66%–68%. The last may cause a rather narrow width for the d* which, together with the quantum numbers and our calculated mass, is consistent with the newly observed resonance-like structure(M ≈2380 Me V, Γ≈70 Me V) in double-pionic fusion reactions reported by the WASA-at-COSY Collaboration.     

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.     

The Ξ~* K and ?η Interaction Within a Chiral Unitary Approach

In this work we study the interaction of the coupled channels ?η and Ξ* ˉK within the chiral unitary approach.The systems under consideration have total isospins 0,strangeness S =-3,and spin 3/2.We study the s wave interaction which implies that the possible resonances generated in the system can have spin-parity JP= 3/2-.The unitary amplitudes in coupled channels develop poles that can be associated with some known baryonic resonances.We find there is a dynamically generated 3/2-? state with mass around 1800 Me V,which is in agreement with the predictions of the five-quark model.     

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.     

Double heavy tri-hadron bound state via delocalized π bond

The number of exotic candidates that are beyond the conventional quark model has increased dramatically over recent decades.Some of these can be viewed as analogues of the deuteron.Similarly,the existence of the triton indicates that bound states formed by three hadrons could also exist.To illustrate this possibility,we study the DD~*K and■systems using the Born-Oppenheimer approximation.To leading order,only one-pion exchange potentials are considered.This means that the three constituents share one virtual pion.This is similar to the role of the delocalizedπbond for the formation of benzene in chemistry.After solving the Schr?dinger equation,we find two three-body DD~*K and■ bound states with masses 4317.92~_(-6.55)(+6.13)Me V and11013.65_(-8.84)~(+8.49)Me V,respectively.The masses of their ■and■ analogues are 4317.92~_(-6.55)(+6.13)Me V and11013.65_(-9.02)~(+8.68)Me V,respectively.From the experimental side,the ■bound state could be found by analyzing the current world data on the B→J/ψππKprocess,by focusing on the J/ψπK channel.     

Mixing of scalar meson and baryon-baryon interaction

At quark level,we study the effect of ideal mixing of singlet σ 0 and octet σ 8 scalar mesons on baryon-baryon interaction in the chiral SU(3) quark model.We solve the resonating group method equation for scattering process and bound state.The results show that the binding energy of deuteron and nucleonnucleon and hyperon-nucleon scattering data can be reasonably described for ideal mixing.Taking the same parameters we used in the scattering calculation,we further investigate the possible dibaryons and find the binding energy of (ΩΩ) ST =00 and (Ξ *Ω) ST =0 1 2 can be reduced a lot for ideal mixing.     

Triply heavy baryons in the constituent quark model

The constituent quark model is used to compute the ground and excited state masses of QQQ baryons containing either c or b quarks.The quark model parameters previously used to describe the properties of charmonium and bottomonium states were used in this analysis.The non-relativistic three-body bound state problem is solved by means of the Gaussian expansion method which provides sufficient accuracy and simplifies the subsequent evaluation of the matrix elements.Several low-lying states with quantum numbers J^P=1/2^±,3/2^±,5/2^±and 7/2^+are reported.We compare the results with those obtained by the other theoretical formalisms.There is a general agreement for the mass of the ground state in each sector of triply heavy baryons.However,the situation is more puzzling for the excited states,and appropriate comments about the most relevant features of our comparison are given.     

Energy loss of charm quarks from J/ψ production incold nuclear matter

J/ψ suppression in p-A collisions is studied by considering the nuclear effects on parton distribution, energy loss of beam proton and the finial state energy loss of color octet cc. The leading-order computations for J/ψ production cross-section ratios R_W/Be(x_F) are presented and compared with the selected E866 experimental data with the cc remaining colored on its entire path in the medium. It is shown that the combination of the different nuclear effects accounts quite well for the observed J/ψ suppression in the experimental data. It is found that the J/ψ suppression on R_W/Be(x_F) from the initial state nuclear effects is more important than that induced by the energy loss of color octet cc in the large x_F region. Whether the cc pair energy loss is linear or quadratic with the path length is not determined. The obtained cc pair energy loss per unit path length α=2.78±0.81 GeV/fm, which indicates that the heavy quark in cold nuclear matter can lose more energy compared to the outgoing light quark.     

Possible hadronic molecular states composed of S-wave heavy-light mesons

We perform a systematical study of possible molecular states composed of the S wave heavy light mesons,where the S–D mixing and η-η' mixing are explicitly included.Our calculation indicates that the observed X(3872) could be a loosely shallow molecular state composed of D*+ h.c,while neither Z_c(3900)/Z_c(4020) nor Z_b(10610)/Z_b(10650) is supported to be a molecule.Some observed possible molecular states are predicted,which could be searched for by further experimental measurements.     

Study of Σ~*-Δ Interactions

We study the Σ~*-Δ interaction in the chiral SU(3) quark model and in the extended chiral SU(3) quark model.In these two models,the short-range interaction mechanism are totally different,one is from the one-gluon exchange and another is from the vector meson exchange.The possible reasons of forming strangeness-1 bound states are given.Comparisons between the cases with and without quark exchange effect are made.The results show the quark exchange effect does give attractions to (Σ~*Δ)_(ST)=0 5/2 and (Σ~*Δ)_(ST)=3 1/2 systems,which means the special symmetry is important.Also,we make some analysis on chiral field effect,our results show that the σ exchange dominantly provides the attractive interaction for these two states.     

On the chiral covariant approach to ρρ scattering

We examine in detail a recent work(D. Gülmez, U. G. Mei?ner and J. A. Oller, Eur. Phys. J. C,77: 460(2017)), where improvements to make ρρ scattering relativistically covariant are made. The paper has the remarkable conclusion that the J =2 state disappears with a potential which is much more attractive than for J =0,where a bound state is found. We trace this abnormal conclusion to the fact that an "on-shell" factorization of the potential is done in a region where this potential is singular and develops a large discontinuous and unphysical imaginary part. A method is developed, evaluating the loops with full ρ propagators, and we show that they do not develop singularities and do not have an imaginary part below threshold. With this result for the loops we define an effective potential, which when used with the Bethe-Salpeter equation provides a state with J =2 around the energy of the f_2(1270). In addition, the coupling of the state to ρρ is evaluated and we find that this coupling and the T matrix around the energy of the bound state are remarkably similar to those obtained with a drastic approximation used previously, in which the q~2 terms of the propagators of the exchanged ρ mesons are dropped, once the cut-off in the ρρ loop function is tuned to reproduce the bound state at the same energy.