Quark-quark Interaction Research Articles

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 proved successful 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 Q^2, which may be useful, for example, in building quark-diquark models of nucleons.

Adler function and hadronic contribution to the muon g-2 in a nonlocal chiral quark model

The behavior of the vector Adler function at spacelike momenta is studied in the framework of a covariant chiral quark model with instantonlike quark-quark interaction. This function describes the transition between the high-energy asymptotically free region of almost massless current quarks to the low-energy hadronized regime with massive constituent quarks. The model reproduces the Adler function and $V\ensuremath{-}A$ correlator extracted from the ALEPH and OPAL data on hadronic $\ensuremath{\tau}$ lepton decays, transformed into the Euclidean domain via dispersion relations. The leading order contribution from the hadronic part of the photon vacuum polarization to the anomalous magnetic moment of the muon, ${a}_{\ensuremath{\mu}}^{\mathrm{h}\mathrm{v}\mathrm{p}(1)}$, is estimated.

Chemical Potential Dependence of Dressed-Quark Propagator**The project supported in part by National Natural Science Foundation of China under Grant Nos. 10175033 and 10135030 and the Research Fund for the Doctoral Program of Higher Education of China under Grant No. 20030284009

A method for obtaining the low chemical potential dependence of the dressed quark propagator from an effective quark-quark interaction model is developed. Of particular interest here is to give a general recipe to find without arbitrariness the solution representing the “Wigner” phase at non-zero chemical potential for the purpose of studying QCD phase structure.

Studying the role of the 't Hooft interaction in QCD, by means of lattice simulations

We report on a recent investigation on the dynamics of light quarks, at intermediate and low energy. By measuring some appropriate correlation functions on the lattice, it is possible to probe the Dirac and flavor structure of the non-perturbative quark-quark interaction and look directly for signatures of the 't Hooft Lagrangian. Results obtained with chiral fermions strongly support the instanton picture and the phenomenological parameters of the Instanton Liquid Model

Vector Susceptibility of QCD Vacuum from an Effective Quark-Quark Interaction**The project supported in part by National Natural Science Foundation of China under Grant Nos. 10175033 and 10135030

A new approach for calculating vacuum susceptibilities from an effective quark-quark interaction model is derived. As a special case, the vector vacuum susceptibility is calculated. A comparison with the results of the previous approaches is given.

Baryon spectroscopy with the CB-ELSA detector at ELSA

The investigation of the excitation spectrum of baryons provides important information on many open questions in baryon spectroscopy. The key to any progress is the identification of the effective degrees of freedom leading to a qualitative understanding of strong QCD. The problem of missing resonances predicted by quark models is discussed on the basis of recent experimental results of the CB-ELSA experiment at the e− accelerator ELSA in Bonn. First hints for resonance production are given and cascades of the type \({N^{ * * }}\left( {{\Delta ^{ * * }}} \right) \to {N^ * }\left( {{\Delta ^ * }} \right) \to p{\pi ^0}{\pi ^0}\left( {p{\pi ^0}\eta } \right) \) are observed. Indications for a Δ-resonance around 1900 MeV are seen. The latter is particularly interesting if it had negative parity because a confirmation of this state would be in contradiction with almost all constituent quark models, (S. Capstick, N. Isgur, Phys. Rev. D 34, 2809 (1986); U. Lohring et al., Eur. Phys. J. A 10, 309 (2001)) for instance. Both, the quark models using one-gluon exchange and the quark model using instanton-induced forces as short-range residual quark-quark interaction predict the three states Δ 5/2− (1930), Δ 3/2− (1940) and Δ 1/2− (1900)at masses in the 2200 MeV region.

Evidence for instanton-induced dynamics from lattice QCD.

We perform a study of the nonperturbative dynamics of the light-quark sector of QCD, based on some recent results of lattice simulations with chiral fermions. We analyze some correlators that are designed to probe the Dirac structure of the quark-quark interaction at different scales. We show that, in the nonperturbative regime, such an interaction contains very large scalar and pseudoscalar components. We observe quantitative agreement between lattice QCD results and the predictions of the instanton liquid model. Moreover, we study how the quark-quark interaction is modified, when quark loops are suppressed. We observe a dramatic effect related to the loss of unitarity, which is naturally explained in the instanton picture. Such an effect cannot be explained in a Dyson-Schwinger equations (DSE) approach, if one assumes a vector quark-gluon coupling.

Vector and axial-vector correlators in a non-local chiral quark model

The behavior of nonperturbative parts of the isovector-vector and isovector and isosinglet axial-vector correlators at Euclidean momenta is studied in the framework of a covariant chiral quark model with nonlocal quark-quark interactions. The gauge covariance is ensured with the help of the P-exponents, with the corresponding modification of the quark-current interaction vertices taken into account. The low- and high-momentum behavior of the correlators is compared with the chiral perturbation theory and with the QCD operator product expansion, respectively. The V-A combination of the correlators obtained in the model reproduces quantitatively the ALEPH data on hadronic \tau decays, transformed into the Euclidean domain via dispersion relations. The predictions for the electromagnetic \pi^\pm - \pi^0 mass difference and for the pion electric polarizability are also in agreement with the experimental values. The topological susceptibility of the vacuum is evaluated as a function of the momentum, and its first moment is predicted to be \chi'(0)\approx (50 MeV)^2. In addition, the fulfillment of the Crewther theorem is demonstrated.

Transport properties and equation of state of quark-nuclear matter

Transport equations for composite nucleons and deconfined quarks in quark-nuclear matter (QNM) are derived. QNM is a many-body system containing hadrons and deconfined quarks. The starting point is a microscopic quark-meson coupling (QMC) Hamiltonian with a density-dependent quark-quark interaction. An effective quark-hadron Hamiltonian containing canonical hadron and quark field operators is constructed using a mapping procedure. For high densities, the effective Hamiltonian contains interactions that lead to quark deconfinement. Transport equations of the Ueling-Ullenbeck-Vlasov type for quarks and nucleons are obtained using standard many-body techniques with the effective quark-hadron Hamiltonian. I Introduction The study of the properties of high density hadronic matter is one of the most important problems in contemporary physics. The possibility of creating in laboratory a new state of matter through collisions of heavy nuclei has become feasible in recent years, with widespread opportunities for understanding several aspects of the strong interactions and matter in superdense stars and at the origin of the universe. One of the central questions in this field is the identification of the appropriate degrees of freedom to describe the different phases of hadronic matter. At densities much higher than the nuclear saturation density, a phase of deconfined matter composed of quarks and gluons is expected to occur. The study of the properties of such a state is possible with the methods of perturbative quantum chromodynamics (QCD). On the other hand, the study of matter at densities not much higher than the saturation density of nuclear matter - like the one existing in dense stars - is very complicated. The complication is due to the fact that this phase of matter is characterized by nonperturbative QCD phenomena and the use of tractable models and drastic approximations is presently the only practical way of tackling the problem. The quark-meson coupling (QMC) model [1] is a very useful model to study the different phases of hadronic matter. It is formulated in terms of quark-gluon degrees of freedom and is devised in such a way to incorporate in an explicit way hadron structure in the nuclear many-body problem. In this model, low-density hadronic matter is described as a system of independent baryons interacting through effective scalar- and vector-meson degrees of freedom which couple directly to the quarks. At very high density the quarks and gluons become deconfined and the entire system is confined by a bag, or potential. For a list of references and recent work, see Ref. [2].

Diquark interaction and gaps for color superconductivity

Using flow equations, we derive an effective quark-quark interaction and obtain the coupled set of gap equations for the condensates of the CFL phase of massless N f = 3 dense QCD. The formalism developed here enables one to consider more general case of nonzero s-quark mass.

Analytic proof that the quark model complies with partially conserved axial current theorems

The Weinberg theorem, the Adler self-consistency zero, the Goldberger and Treiman relation, and the Gell-Mann, Oakes, and Renner relation are proved analytically in full detail for quark models. These proofs are independent of the particular quark-quark interaction, and they are displayed with Feynman diagrams in a compact notation. I assume the ladder truncation, which is natural in the quark model, and also detail the diagrams that must be included in each relation. Off mass shell and finite size effects are included in the quark-antiquark pion Bethe-Salpeter vertices. The axial and vector Ward identities, for the quark propagator and for the ladder, exactly cancel any model dependence.

Small Current Quark Mass Effects on Dressed-Quark Propagator in an Effective Quark-Quark Interaction Model**The project supported in part by National Natural Science Foundation of China under Grant Nos. 19975062, 10175033, and 10135030

A method for obtaining the small current quark mass dependence of the dressed quark propagator from an effective quark-quark interaction model is developed. Within this approach the small current quark mass effects on dressed-quark propagator have been studied. A comparison with previous results is given.

Chemical Potential Dependence of the Dressed-Quark Propagator from an Effective Quark-Quark Interaction**The project supported in part by National Natural Science Foundation of China under Grant Nos. 19975062, 10175033, and 10135030

We exhibit a method for obtaining the low chemical potential dependence of the dressed quark propagator from an effective quark-quark interaction model. Within this approach we explore the chemical potential dependence of the dressed-quark propagator, which provides a means of determining the behavior of the chiral and deconfinement order parameters. A comparison with the results of previous researches is given.

MicroscopicNN→NN*(1440)transition potential: Determination ofπNN*(1440)andσNN*(1440)coupling constants

A $N\stackrel{\ensuremath{\rightarrow}}{N}{\mathrm{NN}}^{*}(1440)$ transition potential, based on an effective quark-quark interaction and a constituent quark cluster model for baryons, is derived in the Born-Oppenheimer approach. The potential shows significant differences with respect to those obtained by a direct scaling of the nucleon-nucleon interaction. From its asymptotic behavior we extract the values of $\ensuremath{\pi}{\mathrm{NN}}^{*}(1440)$ and $\ensuremath{\sigma}{\mathrm{NN}}^{*}(1440)$ coupling constants in a particular coupling scheme.

DIRECT INTERACTION BETWEEN BARYONS AND THE EXTENSION OF THE RELATIVISTIC MEAN FIELD THEORY FOR NUCLEAR MATTER

We propose a new version of the relativistic mean field theory for nuclear matter. The theory is based on an effective relativistic Lagrangian, in which, besides interactions via exchange mesons, baryons also interact with each other directly. The direct interaction is introduced to represent the compositeness of the baryon and to simulate the quark-quark interaction between them.

Interactions of some decuplet baryons in the quark cluster model

In the framework of the resonating-group method, the interactions of decuplet baryon-baryon systems with strangeness numbers $s=\ensuremath{-}1$ and $s=\ensuremath{-}5$ are investigated by employing the chiral SU(3) quark model. The effective baryon-baryon interactions deduced from quark-quark interactions and scattering cross sections of the ${\ensuremath{\Sigma}}^{*}\ensuremath{\Delta}$ and ${\ensuremath{\Xi}}^{*}\ensuremath{\Omega}$ systems are calculated.

Testing the quark cluster model in nucleon-nucleon scattering

The description of the short-range part of the nucleon-nucleon forces in terms of quark degrees of freedom is tested against experimental observables. We consider, for this purpose, a model where the short-range part of the forces is given by the quark cluster model and the long- and medium-range forces by well established meson exchanges. The investigation is performed using different quark cluster models coming from different sets of quark-quark interactions. The predictions of this model are compared not only with the phase shifts but also directly with the experimental observables. Agreement with the existing $\mathrm{pp}$ and $\mathrm{np}$ world set of data is poor. This suggests that the current description of the nucleon-nucleon interaction, at short distances, in the framework of the nonrelativistic quark models, is at present only qualitative.

Quark-model based study of the triton binding energy

The three-nucleon bound state problem is studied employing a nucleon-nucleon potential obtained from a basic quark-quark interaction in a five-channel Faddeev calculation. The obtained triton binding energy is comparable to those predicted by conventional models of the $NN$ force.

Effect of higher orbital angular momenta in the baryon spectrum

We have performed a Faddeev calculation of the baryon spectrum for the chiral constituent quark model including higher orbital angular momentum states. We have found that the effect of these states is important, although a description of the baryon spectrum of the same quality as the one given by including only the lowest-order configurations can be obtained. We have studied the effect of the pseudoscalar quark-quark interaction on the relative position of the positive- and negative-parity excitations of the nucleon as well as the effect of varying the strength of the color-magnetic interaction.

Quark model study of the η photo-production:

An extensive and systematic study of the recent eta photoproduction data up to 1.2 GeV is presented within a chiral constituent quark model. A model embodying all known nucleonic resonances shows clear need for a yet undiscovered third S11 resonance in the second resonance region, for which we determine the mass (1.729 GeV) and the total width (183 MeV). Furthermore, we extract the configuration mixing angles, an important property of the quark-quark interaction in the quark model, for the resonances S11(1535) and S11(1650), as well as for the resonances D13(1520) and D13(1700). Our results agree well with the quark model predictions. In addition, the partial eta N decay widths and/or the photo-excitation helicity amplitudes for the nucleonic resonances S11(1535), S11(1650), P11(1710), P13(1720), D13(1520), D13(1700), D15(1675), and F15(1680) are also obtained in this approach.