Discussions on the stability of diquarks

Since the birth of the quark model, the diquark, which is composed of two quarks, has been considered as a substantial structure of a color anti-triplet. This is not only a mathematical simplification for dealing with baryons, but also provides a physical picture where the diquark would behave as a whole object. It is natural to ask whether such a structure is sufficiently stable against external disturbance. The mass spectra of the ground states of the scalar and axial-vector diquarks, which are composed of two-light （L-L）, one-light-one-heavy （H-L） and two-heavy （H-H） quarks, respectively, have been calculated in terms of the QCD sum rules. We suggest a criterion as the quantitative standard for the stability of the diquark. It is the gap between the masses of the diquark and x/~ where so is the threshold of the excited states and continuity, namely the larger the gap is, the more stable the diquark would be. In this work, we calculate the masses of the H-H type to complete the series of the spectra of the ground state diquarks. However, as the criterion being taken, we find that all the gaps for the various diquarks are within a small range. In particular, the gap for the diquark with two heavy quarks, which is believed to be a stable structure, is slightly smaller than that of the other two types of diquarks. Therefore we conclude that because of the large theoretical uncertainty, we cannot use the numerical results obtained with the QCD sum rules to assess the stability of diquarks, but need to invoke other theoretical framework.

Non-Perturbative Analysis of Various Mass Generation by Gluonic Dressing Effect with the Schwinger-Dyson Formalism in QCD

As a topic of “quantum color dynamics”, we study various mass generation of colored particles and gluonic dressing effect in a non-perturbative manner, using the Schwinger-Dyson (SD) formalism in (scalar) QCD. First, we review dynamical quark-mass generation in QCD in the SD approach as a typical fermion-mass generation via spontaneous chiral-symmetry breaking. Second, using the SD formalism for scalar QCD, we investigate the scalar diquark, a bound-state-like object of two quarks, and its mass generation, which is clearly non-chiral-origin. Here, the scalar diquark is treated as an extended colored scalar field, like a meson in effective hadron models, and its effective size R is introduced as a form factor. As a diagrammatical difference, the SD equation for the scalar diquark has an additional 4-point interaction term, in comparison with the single quark case. The diquark size R is taken to be smaller than a hadron, R ~ 1 fm, and larger than a constituent quark, R ~ 0.3 fm. We find that the compact diquark with R ~ 0.3 fm has a large effective mass of about 900 MeV, and therefore such a compact diquark is not acceptable in effective models for hadrons. We also consider the artificial removal of 3- and 4-point interaction, respectively, to see the role of each term, and find that the 4-point interaction plays the dominant role of the diquark self-energy. From the above two different cases, quarks and diquarks, we guess that the mass generation of colored particles is a general result of non-perturbative gluonic dressing effect.

Masses and Widths of Light Scalar Mesons in Chiral Perturbation Theory

基于 diquark 模型，我们假设轻分级的介子是 q 22 状态而非 q。chiral 为轻分级的介子的有效 Lagrangian 被构造，并且集体关系被获得：isotriplet (0) 和 isosinglet (f 0) 是最重并且是退化的， isodoublets (κ ) 更重，另外的 isosinglet (σ ) 最轻；并且 2M κ2= M a0 2+ M σ2 。用为 0 和 σ 质量的试验性的价值，我们获得 M κ= 794 兆电子伏，它与试验性的价值一致。然后拿 Γ (00→ ηπ0)= 90 兆电子伏和 Γ (f 00→ π 0π0)= 20 兆电子伏，我们得到 σ 的宽度：Γ (σ → π +π-)= 150 兆电子伏。

Temperature Dependent Diquark and Baryon Masses

Temperature dependence of diquark mass has been investigated in the frame work of the quasi particle diquark model. The effective mass of the diquark has been suggested to have a temperature dependence which shows a power law behavior. The variation of the diquark mass with temperature has been studied. A decrease in effective mass at temperature T Tc, where Tc is the critical temperature has been observed. Some features of the phase transition have been discussed. The phase transition is found to be of second order. Temperature variation of baryon masses has also been studied. The results are compared and discussed with available works.

Nucleon in Nuclear Matter

The modification of the properties of nucleon in nuclear medium has been investigated in the context of flux tube model. A nucleon has been described as diquark-quark system connected by flux tube and quasi particle diquark model has been used to describe the diquak constituting the nucleon. The modification of incompressiblity, the Roper resonance etc in the nuclear medium have been investigated. The results are compared with recent experimental and theoretical predictions. Some interesting observations are made.

On the Ratios Dark Matter (Energy)/Ordinary Matter ≈5.4(13.6) in the Universe

An upper limit of the average ratio dark matter/ordinary matter in galaxies is estimated to be 8.4, in agreement with the observed ratio 5.4. Upper limit of the average ratio dark energy/ordinary matter for slowly moving protons in the outer parts of the universe is estimated to be 8.4, much less than the observed ratio 13.6. The discrepancy is tentatively attributed to that the bulk of the protons in these outer parts of the universe moves fastly and their contribution to dark energy has not been estimated. The positive and negative relative energies between the diquark and quark in the proton play the roles of dark energy and dark matter, respectively.

Diquark mass differences from unquenched lattice QCD

We calculate diquark correlation functions in the Landau gauge on the lattice using overlap valence quarks and 2＋1flavor domain wall fermion configurations. Quark masses are extracted from the scalar part of quark propagators in the Landau gauge. The scalar diquark quark mass difference and axial vector scalar diquark mass difference are obtained for diquarks composed of two light quarks and of a strange and a light quark. The light sea quark mass dependence of the results is examined. Two lattice spacings are used to check the discretization effects. The coarse and fine lattices are of sizes 24^3 ×64 and 32^3 ×64 with inverse spacings 1/a= 1.75（4） GeV and 2.33（5） GeV, respectively.

Phase diagram of two-color QCD matter at finite baryon and axial isospin densities

We study the two-color QCD matter with two fundamental quark flavors using the chiral perturbation theory and the Nambu-Jona-Lasinio(NJL)model.The effective Lagrangian is derived in terms of mesons and baryons,i.e.diquarks.The low lying excitations lie in the extended SU(4)flavor symmetry space.We compute the leading order terms of the Lagrangian as a function of the baryon and axial isospin densities.After numerically solving the gap equations in the two-color NJL model,the phase diagram is obtained in the μ−ν5 plane.

Influences of magnetic field on the coexistence of diquark and chiral condensates in the Nambu-Jona-Lasinio model with axial anomaly

In this paper,we study the influences of magnetic fields on the coexistence of diquark and chiral condensates in an extended Nambu-Jona-Lasinio model with QCD axial anomaly,as it relates to color-flavor-locked quark matter.Due to the coupling of rotated-charged quarks to magneticfields,diquark condensates become split,and the coexistence region is thus superseded in favor of a specific diquark Bose-Einstein condensation(BEC),denoted as the BECIphase.For strong magnetic fields,we find that the BECItransition is pushed to larger quark chemical potentials.The effect of magnetic catalysis tends to disrupt the BEC-BCS(Bardeen-Cooper-Schrieffer)crossover predicted in previous works.For intermediate fields,the effect of inverse magnetic catalysis is observed,and the axial-anomaly-induced phase structure is essentially unchanged.

Magnetic moments of hidden-charm strange pentaquark states

In this study,the magnetic moments of hidden-charm strange pentaquark states with quantum numbers J^(P)=1^(±)/2,3^(±)/2,5^(±)/2,and 7^(+)/2 are calculated in the molecular,diquark-diquark-antiquark,and diquark-triquark models.The numerical results demonstrate that the magnetic moments change for different spin-orbit couplings within the same model and when involving different models with the same angular momentum.

Study of heavy-light hadrons within a flux tube model

A classic mass loaded flux tube model and the diquark picture are employed to explore both mesons and baryons. The spectrum of Λc＋ baryons and Ds mesons is systematically obtained. The spin-orbit interaction in Ds was simplified as an L·S coupling. The spin-orbit interaction in Λc was simplified as a Jl ·Jc coupling. The predicted masses are consistent with the latest experiments.

D and D_s 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.

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.

Can X(5568) be a tetraquark state?

Very recently, the D0 collaboration has reported the observation of a narrow structure, X（5568）, in the decay process X（5568）→ Bs^0π^±using the 10.4fb^-1 data of pp collision at √s= 1.96 TeV. This structure is of great interest since it is the first hadronic state with four different valence quark flavors, b, s, u, d. In this work,we investigate tetraquarks with four different quark flavors. Based on the diquark-antidiquark scheme, we study the spectroscopy of the tetraquarks with one heavy bottom/charm quark and three light quarks. We find that the lowest-lying S-wave state, a tetraquark with the flavor [su][bd] and the spin-parity J^P= 0^＋, is about 150 MeV higher than the X（5568）. Further detailed experimental and theoretical studies of the spectrum, production and decays of tetraquark states with four different flavors are vital to gain a better understanding of the nature and classification of hadron exotic states.

J^P assignments of Λ_c^+ baryons

The ＂good＂ diquark is employed to study A＋ baryons within a mass loaded flux tube model. The study indicates that all A＋ baryons candidates in the 2008 review by the Particle Data Group （PDG） are well described in the mass loaded flux model. The quantum numbers JP of these A＋ candidates are assigned. If Ac（2765）＋ is an orbitally excited A＋, it is likely the JP=3/2＋one. If ∧c（2765）＋ is an orbitally excited ∑c, there ought to be another JP=3/2＋∧c＋with mass ≈2770 MeV. In the model, there exists no JP=1/2＋∧c＋（≈2700）predicted in existing literature. Ac （2940）＋ is very possible the orbitally excited baryon with

Charmed Baryon in Diquark Model

A diquark model is used to investigate single-charmed baryons. In this model,baryon is composed of two diquarks and an antiquark. Masses of lowest lying states with JP=1/2± are obtained. Baryons in our results are as heavy as other theoretic predictions and we suggest that the five-quark components should be considered in any three-quark model for studying the charmed baryons.