Interplay Between Quark-Antiquark and Diquark Condensates in Vacuum in a Two-Flavor Nambu-Jona-Lasinio Model

By means of a relativistic effective potential, we analytically research competition between the quark- antiquark condensates （qq） and the diquark condensates （qq） in vacuum in ground state of a two-flavor Nambu Jona Lasinio （NJL） model and obtain the Gs-Hs phase diagram, where Gs and Hs are the respective four-fermion coupling constants in scalar quark-antiquark channel and scalar color anti-triplet diquark channel. The results show that, in the chiral limit, there is only the pure （qq） phase when Gs/Hs 〉 2/3, and as Gs/Hs decreases to 2/3 〉 Gs/Hs ≥ 0 one will first have a coexistence phase of the condensates （qq） and （qq） and then a pure （qq） phase. In non-zero bare quark mass case, the critical value of Gs/Hs at which the pure （qq） phase will transfer to the coexistence phase of the condensates （qq） and （qq） will be less than 2/3. Our theoretical results, combined with present phenomenological fact that there is no diquark condensates in the vacuum of QCD, will also impose a real restriction to any given two-flavor NJL model which is intended to simulate QCD, i.e. in such model the resulting sma/lest ratio Gs/Hs after the Fierz transformations in the Hartree approximation must be larger than 2/3. A few phenomenological QCD-like NJL models are checked and analyzed.

Spectra of Free Diquark in the Bethe-Salpeter Approach

In this work, we employ the Bethe-Salpeter （B-S） equation to investigate the spectra of free diquarks and their B-S wave functions. We find that the B-S approach can be consistently applied to study the diqaurks with two heavy quarks or one heavy and one light quarks, but for two light-quark systems, the results are not reliable. There are a few free parameters in the whole scenario which can only be fixed phenomenologically. Thus, to determine them, one has to study baryons which are composed of quarks and diquarks.

Ground State Mass Spectrum for Scalar Diquarks with Bethe-Salpeter Equation

In this article, we study the structures of the pseudoscalar mesons π, K and the scalar diquarks U^a, D^a, Sa in the framework of the coupled rainbow Schwinger-Dyson equation and ladder Bethe-Salpeter equation with the confining effective potential. The u, d, s quarks have small current masses, and the renormalization is very large, the mass poles in the timelike region are absent which implements confinement naturally. The Bethe-Salpeter wavefunctions of the pseudoscalar mesons π, K, and the scalar diquarks U^a, D^a, S^a have the same type （Gaussian type） momentum dependence, center around zero momentum and extend to the energy scale about q^2 = 1 GeV^2, which happens to be the energy scale for the chiral symmetry breaking, the strong interactions in the infrargd region result in bound （or quasl-bound） states. The numerical results for the masses and decay constants of the π and K mesons can reproduce the experimental values, and the ground state masses of the scalar diquarks U^a, D^a, S^a are consistent with the existing theoretical calculations. We suggest a new Lagrangian which may explain the uncertainty of the masses of the scalar diauarks.

A Diquark-Quark Model with Its Use in Nucleon Form Factorst

The nucleon electromagnetic form factors are investigated within a simple diquark-quark model using the light-front formalism. In this model, baryon is described as a bound state of one quark and one clustering diquark. The calculational results are compared with the experimental ones. We also regard the quarks in a baryon as pointlike constituent quarks.

Quark-Antiquark and Diquark Condensates in Vacuum in a 2D Two-Flavor Gross-Neveu Model

The analysis based on the renormalized effective potential indicates that, similar to in the 4D two-flavor Nambu-Jona-Lasinio （NJL） model, in a 2D two-flavor Gross-Neveu model, the interplay between the quark-antiquark and the diquark ,condensates in vacuum also depends on Gs/Hs, the ratio of the coupling constants in scalar quarkantiquark and scalar diquark channel. Only the pure quark-antiquark condensates exist if Gs/Hs 〉 2/3, which is just the ratio of the color numbers of the quarks participating in the diquark and quark-antiquark condensates. The two condensates will coexist if 0 〈 Gs/Hs 〈 2/3. However, different from the 4D NJL model, the pure diquark condensates arise only at Gs/Hs = 0 and are not in a possibly finite region of Gs/Hs below 2/3.

Quark-Antiquark and Diquark Condensates in Vacuum in Two-Flavor Four-Fermion Interaction Models with Any Color Number N_c

The color number Nc-dependence of the interplay between quark-antiquark condensates （q^-q） and diquark condensates （qq） in vacuum in two-flavor four-fermion interaction models is researched. The results show that the Gs-Hs （the coupling constant of scalar （q^-q）2-scalar （qq）2 channel） phase diagrams will be qualitatively consistent with the case of Nc = 3 as Nc varies in 4D Nambu-Jona-Lasinio model and 219 Gross Neveu （GN） model, However, in 3D GN model, the behavior of the Gs-Hp （the coupling constant of pseudoscalar （qq）^2 channel） phase diagram will obviously depend on No. The known characteristic that a 3D GN model does not have the coexistence phase of the condensates （q^-q） and （qq） is proven to appear only in the case of Nc ≤ 4. In all the models, the regions occupied by the phases containing the diquark condensates （qq） in corresponding phase diagrams will gradually decrease as Nc grows up and finally go to zero if Nc → ∞, i.e. in this limit only the pure （q^-q） phase could exist.

Quark-Antiquark and Diquark Condensates in Vacuum in a 3D Two-Flavor Gross-Neveu Model

The effective potential analysis indicates that, in a 3D two-flavor Gross-Neveu model in vacuum, depending on whether Gs/Hp is less or bigger than the critical value 2/3, where G s and H p are respectively the coupling constants of scalar quark-antiquark channel and pseudoscalar diquark channel, the system will have the ground state with pure diquark condensates or with pure quark-antiquark condensates, but never with coexistence of the two forms of condensates. The similarities and differences in the interplay between the quark-antiquark and the diquark condensates in vacuum in the 2D, 3D and 4D two-flavor four-fermion interaction models are summarized.

Non—spectator Diquark Effiects on Lifetimes of Λb,Ωb（＊） and Weak Decay Rates of ∑bΞb（＊）

The difference of and indicates the role of the light flavors. We calculate the lifetimes of -meson and based on the weak effective Hamiltonian while assuming the heavy baryon is constructed by a heavy -quark and a diquark containing two light quarks. In this scenario, we use the information of the measured ratio as input to predict rates of the inclusive weak decays of and into non-bottom final states. We find that these rates of and are much larger than those of -mesons and . We also give the predictions for the lifetimes of and . Phenomenological implication of our result is discussed.

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.

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.

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.

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.

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.

Analysis of the Light-Flavor Scalar and Axial-Vector Diquark States with QCD Sum Rules

In this article, we study the light-flavor scalar and a^ial-vector diquark states in the vacuum and in the nuclear matter using the QCD sum rules in a systematic way, and make reasonable predictions for their masses in the vacuum and in the nuclear matter.

Quark-diquark model description for double charm baryons

We report here the mass spectrum and magnetic moments of ccq（q ∈ u,d,s） systems in the potential model framework by assuming the inter-quark potential as the colour coulomb plus power form with power index ν varying between 0.1 to 2.0.Here the two charm quarks are considered for the diquark states.The conventional one gluon exchange interaction has been employed to get the hyperfine and the fine structure between different states.We have predicted many low-lying states whose experimental verification can exclusively support the quark-diquark structure of the baryons.

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.

XYZ新强子态的研究进展

分析了高能物理实验产生XYZ新强子态的主要机制,总结了已发现XYZ新强子态的质量、量子数、产生和衰变过程,并讨论了目前人们对X(3872)和Z±粒子提出的各种理论解释.

小横动量介子与双夸克对R值的贡献

考虑小横动量介子与双夸克的贡献后，对Ｒ＝σ＿Ｌ／σ＿Ｔ值进行了计算，所得结果在整个ｘ区与实验数据相符合．

负宇称五夸克态

在Jaffe和Wilczek模型中存在负宇称的五夸克八重态和单态,这些五夸克态中的两个双夸克之间没有轨道激发,这些五夸克态比Θ+的质量要轻,利用Jaffe和Wilc-zek模型计算了Jp=12-的五夸克八重态和单态的质量与磁矩,结果表明与普通重子有轨道激发(l=1)的质量接近,得到一些重要的质量和磁矩关系式,这些五夸克态的质量范围在1360MeV和1540MeV之间,建议在实验上寻找Jp=1/2-的五夸克八重态和单态,其中有两个Jp=12-的五夸克态质量在Λ(1405)的附近,建议Λ(1405)是负宇称五夸克的一个候选者,如果将来的实验证实了这些态,将对Jaffe和Wilczek模型是极大的支持。

Masses and Widths of Light Scalar Mesons in Chiral Perturbation Theory

Based on the diquark model, we assume that the light scalar mesons are q^2q^-2 states rather than qq^-. The chiral effective Lagrangian for the light scalar meson is constructed, and the mass relations are obtained： the isotriplet （a0） and the isosinglet （f0） are the heaviest and are degenerate, the isodoublets （κ） are heavier and the other isosinglet （σ） is the lightest; and 2Mκ^2 = Mα0^2＋ Mσ^2. Using experimental value for a0 and σ mass, we obtain Mκ=794 MeV, which is consistent with the experimental value. Then taking Г（a0^0 →ηπ^0） = 90 MeV and Г（f0→π^0π^0） = 20 MeV, we get the width of σ is： Г（σ0→π^＋π^-）= 150 MeV.