Nucleon form factors in a covariant diquark-quark model

In a model where constituent quarks and diquarks interact through quark exchange the Bethe-Salpeter equation in ladder approximation for the nucleon is solved. Quark and diquark confinement is effectively parametrized by choosing appropriately modified propagators. The coupling to external currents is implemented via non-trivial vertex functions for quarks and diquarks to ensure gauge invariance at the constituent level. Nucleon matrix elements are evaluated in a generalized impulse approximation, and electromagnetic, pionic and axial form factors are calculated.     

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 Ua,Da,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 Ua,Da,Sa have the same type (Gaussian type) momentum dependence,center around zero momentum and extend to the energy scale about q2 = 1 GeV2,which happens to be the energy scale for the chiral symmetry breaking,the strong interactions in the infrared region result in bound (or quasi-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 Ua,Da,Sa are consistent with the existing theoretical calculations.We suggest a new Lagrangian which may explain the uncertainty of the masses of the scalar diquarks.     

Mass spectrum of diquarks and mesons in the color–flavor locked phase of dense quark matter

The spectrum of meson and diquark excitations of dense quark matter is considered in the framework of the Nambu–Jona-Lasinio model with three types of massless quarks in the presence of a quark number chemical potential μ. We investigate the effective action of meson and diquark fields both at sufficiently large values of μ>μ_c≈  330 MeV, where the color–flavor locked (CFL) phase is realized, and in the chirally broken phase of quark matter (μ<μ_c). In the latter case all nine pseudoscalar mesons are Nambu–Goldstone (NG) bosons, whereas the mass of the scalar meson nonet is twice the dynamical quark mass. In the chirally broken phase the pseudoscalar diquarks are not allowed to exist as stable particles, but the scalar diquarks might be stable only at a rather strong interaction in the diquark channel. In the case of the CFL phase, all NG bosons of the model are realized as scalar and pseudoscalar diquarks. Moreover, it turns out that massive diquark excitations are unstable for this phase. In particular, for the scalar and pseudoscalar octets of diquark resonances a mass value around 230 MeV was found numerically. In contrast, mesons are stable particles in the CFL phase. Their masses lie in the interval 400–500 MeV for not too large values of μ>μ_c. PACS 11.30.Qc; 12.38.-t; 12.39.-x     

Light and heavy hadron masses in a relativistic quark potential model with diquark clustering

Meson masses are calculated in the quark model with a phenomenological spin-dependent potential of form motivated by QCD. For comparison, the potential is used in two different wave equations, both of which incorporate the feature of relativistic two-body kinematics. The masses of light and heavy pseudoscalar and vector mesons are calculated in the model with only a small number of adjustable parameters, and good qualitative agreement with experiment is obtained. The masses of diquarks are calculated without any additional parameters, using the same potential as for mesons except for a QCD color factor. Then baryon masses are calculated, also without additional parameters, in an approximation in which a baryon is a composite of a quark and a diquark. Again the results are in good qualitative agreement with experiment. Both wave equations yield similar solutions, although there are differences in detail. One distinctive feature of the model is that quark current masses are used as input, and effective constituent quark masses are obtained as a result of the calculation.     

Electromagnetic Properties of Diquarks

Diquark correlations play an important role in hadron physics. The properties of diquarks can be obtained from the corresponding bound-state equation. Using a model for the effective quark-quark interaction that has been proved successfully in the light meson sector, we solve the scalar diquark Bethe-Salpeter equations and use the obtained Bethe-Salpeter amplitudes to compute the diquarks electromagnetic form factors. The scalar ud diquark charge radius is about 8% larger than the pion charge radius, indicating that these diquarks are somewhat larger in size than the corresponding mesons. We also provide analytic fits for the form factor over a moderate range in Q², which may be useful, for example, in building quark-diquark models of nucleons.     

关于Reggeon的结构

从强子组分夸克具有结构的观点出发，根据高能强作用软过程中的最大非微扰强作用反应假定,提出了关于Reggeon(IR)的结构模型.高能时对撞强子中的一对组分夸克-反夸克在最大反应下有一定的几率先分解为非微扰胶子和旋量团(反旋量团).此旋量团对将进一步演化而放射出一系列的非微扰胶子(和夸克对)并最终湮没.将这种过程与其逆向(厄米共轭)过程并合,就可得出有关的IR的场论结构图象.它是以旋量团为竖线,胶子为横线的一系列切割梯形图之和所代表.本文在系统能量大而动量转移很小的多重Regge运动学区间和只保留Ins的领头阶近似下,计算了这组切割梯形图相应的散射振幅,求出了它们的总和,得出了与轻夸克介子对应的典型Regge极点轨迹的简洁表达式,对结果进行了简单的讨论.     

On the Structure of Reggeon

Starting from the point-view that the constituent quark has its own inner structure and according to the hypothesis of the maximum non-perturbative strong interaction reaction which should be obeyed in high energy strong-soft Processes ,we proposed a structure model of the Reggeon(R). In such processes a pair of constituent quark-antiquark in colliding hadrons would individually desociate with certain probahility into a non-perturbative gluon and a spinor-like cluster firstly. The spinor-like clusters will further emit non-perturbative gluons and then annihilate each other. Corresponding to such mechanism the relevant structure of R in the field theory can be represented by summing over a set of cutting ladder diagrams, where the vertical lines are the propagators of spinor-like clusters and the rungs are non-perturbative gluons. In the multi-Regge region where the energy of the system is very large and its momentum transfer│t│is very small, under the approximation that only the leading order logarithm terms of s are preserved, the scattering amplitudes for these cutting ladder diagrams are derived and summed. Thus, a compact formula of the typical Regge pole trajectory of mesons which are composed of light quarks is obtained.     

Calculation of Four-Quark Condensate Beyond Vacuum Saturation Approximation

Based on a modification of theaglobal color symmetry model, we have calculated the four-quark condensate beyond vacuum saturation approximation by including the contribution of r and u mesons. The numerical results show that there is a sizeable correction of the four-quark condensate in comparison with its factorized value using the vacu urn saturation approximation.     

On the confinement of quarks and vector gluons in a superconducting phase

Within a simple model of a self-interacting quark field an attempt is described to introduce diquarks a priori by spontaneous breaking of gauge invariance much in the same way as electron pairs are incorporated by the nonrelativistic BCS theory of superconductivity. This is done because baryons can be regarded as a quark-diquark system. It is shown that quarks with a mass smaller than the invariant mass gap will find it energetically unfavourable to enter a superconducting region. By referring to the Boson transformation method it is argued that bag, respectively, vortex type solutions exist. The quark-quark pairing in the groundstate induces a spontaneous breaking of Lorentz isotropy which, by the Goldstone theorem, leads to automatically confined (abelian) vector gluons of zero mass in the skin region of the hadron. A large anomalous spin-spin coupling among the valence quarks, as required by the π-? mass difference, is likely to be present. It is pointed out that the skin region of mesons and baryons may have a different structure. Solutions where the quark moves freely inside a confined region correspond to the possibility of having a space dependent mass gap.     

A static calculation of radiative decay widths of mesons in a potential model of independent quarks

Taking a relativistic potential model of independent quarks with its parameters determined from a fit to the mass splittings of ground state mesons in the strange, charm and bottom flavor sector, we perform a ‘static’ calculation of decay widths for the radiative transitions of mesons within the conventional picture of photon emission by a confined quark and/or antiquark. The results obtained in most of the cases of light mesons are in an overall agreement with the experimental values. The predictions in heavy meson decays are comparable to those of other model calculations.     

Quark-Quark Correlations in the Nucleon in a Generalized Nambu-Jona-Lasinio Model

We present a relativistic model of the nucleon based upon a quark-diquark structure that emerges from a study of the Nambu-Jona-Lasinio model. Similar calculations, made by other authors, have been carried out after a Wick rotation is performed. These previous calculations have neglected confinement; therefore, the masses of the quarks and diquarks had to be adjusted so that the diquarks and the nucleon were stable, in which case the Wick rotation may be made. In our work, we include a momentum-space model of confinement developed earlier and we are therefore able to carry out the calculation in Minkowski space, after making a number of approximations. We determine the relative admixture of a scalar-isoscalar diquark and an axialvector-isovector diquark dynamically and find that an approximately equal admixture provides a reasonable fit to the nucleon magnetic moments. While the original problem (without approximation) requires the specification of eight scalar functions of two variables, our various approximations allow us to calculate several functions of a single variable. We find that only two of these functions are important. Therefore, we can exhibit a relatively simple relativistic wave function of the nucleon expressed in terms of two wave functions describing the relative motion of the quarks and diquarks. Received December 5, 1995; accepted for publication February 13, 1996     

Higher tetraquark particles

There are strong arguments favoring a four-quark interpretation of sub-GeV light scalar mesons and the diquark–antidiquark body-plan of the tetraquark seems to provide the most convincing picture. The building diquarks of these particles are assumed to be spin zero objects. In this Letter we explore the possibility that radially excited aggregations of spin zero or spin one diquarks might exist and discuss the possibility of the Y(2175)$Y(2175)$ state observed by BaBar and confirmed by BES being one such state.     

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 √s₀ where s₀ 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 exotics in heavy ion collisions

Based on the color–spin interaction in diquarks, we argue that charmed multiquark hadrons are likely to exist. Because of the appreciable number of charm quarks produced in central nucleus–nucleus collisions at ultrarelativistic energies, the production of charmed multiquark hadrons is expected to be enhanced in these collisions. Using both the quark coalescence model and the statistical hadronization model, we estimate the yield of charmed tetraquark mesons, T_cc, and pentaquark baryons, Θ_cs, in heavy ion collisions at RHIC and LHC. We further discuss the decay modes of these charmed exotic hadrons in order to facilitate their detections in experiments. PACS 25.75.Dw; 14.20.Lq; 14.40.Lb     

Analysis of the Nonet Scalar Mesons as Tetraquark States with New QCD Sum Rules

In this article, we take the scalar diquarks as point particles and describe them as basic quantum fields, then introduce the SU(3) color gauge interaction and new vacuum condensates to study the nonet scalar mesons as tetraquark states with the QCD sum rules. Comparing with the conventional quark currents, the diquark currents have the outstanding advantage to satisfy the two criteria of the QCD sum rules more easily.     

THE WAVE EQUATIONS AND MASS SPECTRA OF BARYON STATES IN THE QUARK MODEL

The independent particle approximation is used to treat the bound state problems in the quark model. The solution for meson states obtained in this approximation is the same as that obtained from the Bethe-Salpeter equation. The solution for the baryon states is also obtained. The mass spectra of mesons and baryons determined from these equations are in agreement with the experiment.     

Aspects of the confinement mechanism in Coulomb-gauge QCD

Phenomenological consequences of the infrared singular, instantaneous part of the gluon propagator in the Coulomb gauge are investigated. The corresponding quark Dyson-Schwinger equation is solved, neglecting retardation and transverse gluons and regulating the resulting infrared singularities. While the quark propagator vanishes as the infrared regulator goes to zero, the frequency integral over the quark propagator stays finite and well defined. Solutions of the homogeneous Bethe-Salpeter equation for the pseudoscalar and vector mesons as well as for scalar and axial-vector diquarks are obtained. In the limit of a vanishing infrared regulator the diquark masses diverge, while meson properties and diquark radii remain finite and well defined. These features are interpreted with respect to the resulting aspects of confinement for colored quark-quark correlations.     

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 J~P=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.