Axial-vector Diquark Research Articles

Nucleon mass and pion loops

Poincare' covariant Faddeev equations for the nucleon and Delta are solved to illustrate that an internally consistent description in terms of confined-quark and nonpointlike confined-diquark-correlations can be obtained. pi N-loop induced self-energy corrections to the nucleon's mass are analysed and shown to be independent of whether a pseudoscalar or pseudovector coupling is used. Phenomenological constraints suggest that this self-energy correction reduces the nucleon's mass by up to several hundred MeV. That effect does not qualitatively alter the picture, suggested by the Faddeev equation, that baryons are quark-diquark composites. However, neglecting the pi-loops leads to a quantitative overestimate of the nucleon's axial-vector diquark component.

Axial vector diquark correlations in the nucleon: structure functions and static properties

In order to extract information on the strength of quark–quark correlations in the axial vector (a.v.) diquark channel ( J P =1 +, T=1), we analyze the quark light cone momentum distributions in the nucleon, in particular their flavor dependencies, and the static properties of the nucleon. To construct the nucleon as a relativistic 3-quark bound state, we use a simple “static” approximation to the full Faddeev equation in the Nambu–Jona-Lasinio model, including correlations in the scalar ( J P =0 +, T=0) and a.v. diquark channels. It is shown that the a.v. diquark correlations should be rather weak compared to the scalar ones. From our analysis we extract information on the strength of the correlations as well as on the probability of the a.v. diquark channel.

Parametrizations of quark confinement in production processes

Baryons are described as bound states of quarks and scalar as well as axialvector diquarks. In order to effectively parametrize confinement several ansaetze for the dressing functions of the constituent propagators are used. The corresponding results for electromagnetic and strong form factors differ only slightly. On the other hand observables from production processes show the permissibility of different dressing functions.

Electromagnetic radiation of baryons containing two heavy quarks

The two heavy quarks in a baryon which contains two heavy quarks and a light one, can constitute a scalar or axial vector diquark. We study electromagnetic radiations of such baryons, (i) \Xi_{(bc)_1} -> \Xi_{(bc)_0}+\gamma, (ii) \Xi_{(bc)_1}^* -> \Xi_{(bc)_0}+\gamma, (iii) \Xi_{(bc)_0}^{**}(1/2, l=1) -> \Xi_{(bc)_0}+\gamma, (iv) \Xi_{(bc)_0}^{**}(3/2, l=1) -> \Xi_{(bc)_0}+\gamma and (v) \Xi_{(bc)_0}^{**}(3/2, l=2) -> \Xi_{(bc)_0}+\gamma, where \Xi_{(bc)_{0(1)}}, \Xi^*_{(bc)_1} are S-wave bound states of a heavy scalar or axial vector diquark and a light quark, and \Xi_{(bc)_0}^{**}(l is bigger than 1) are P- or D-wave bound states of a heavy scalar diquark and a light quark. Analysis indicates that these processes can be attributed into two categories and the physical mechanisms which are responsible for them are completely distinct. Measurements can provide a good judgment for the diquark structure and better understanding of the physical picture.

Nucleon properties in the covariant quark-diquark model

In the covariant quark-diquark model the effective Bethe-Salpeter (BS) equations for the nucleon and the Δ are solved including scalar and axial vector diquark correlations. Their quark substructure is effectively taken into account in both, the interaction kernel of the BS equations and the currents employed to calculate nucleon observables. Electromagnetic current conservation is maintained. The electric form factors of proton and neutron match the data. Their magnetic moments improve considerably by including axial vector diquarks and photon induced scalar-axial vector transitions. The isoscalar magnetic moment can be reproduced, the isovector contribution is about 15% too small. The ratio µG E/G M and the axial and strong couplings g A, g πNN, provide an upper bound on the relative importance of axial vector diquarks confirming that scalar diquarks nevertheless describe the dominant 2-quark correlations inside nucleons.

A comparison between relativistic and semi-relativistic treatment in the diquark–quark model

In the diquark–quark model of the nucleon including scalar and axialvector diquarks we compare solutions of the ladder Bethe–Salpeter equation in the instantaneous Salpeter approximation and in the fully covariant (i.e. four-dimensional) treatment. We obtain that the binding energy is severely underestimated in the Salpeter approximation. For the electromagnetic form factors of the nucleon we find that in both approaches the overall shapes of the respective form factors are reasonably similar up to Q 2≈0.4 GeV 2. However, the magnetic moments differ substantially as well as results for the pion–nucleon and the axial coupling of the nucleon.

Nucleons or diquarks: Competition between clustering and color superconductivity in quark matter

We study the instabilities of quark matter in the framework of a generalized Nambu--Jona-Lasinio model, in order to explore possible competition between three-quark clustering to form nucleons and diquark formation leading to color superconductivity. Nucleon and $\Delta$ solutions are obtained for the relativistic Faddeev equation at finite density and their binding energies are compared with those for the scalar and axial-vector diquarks found from the Bethe-Salpeter equation. In a model with interactions in both scalar and axial diquark channels, bound nucleons exist up to nuclear matter density. However, except at densities below about a quarter of that of nuclear matter, we find that scalar diquark formation is energetically favored. This raises the question of whether a realistic phase diagram of baryonic matter can be obtained from any model which does not incorporate color confinement.

Kaon photoproduction and form factors in a covariant and confining diquark-quark model for baryons

Baryons are modeled as bound states of scalar or axialvector diquarks and a constituent quark which interact through quark exchange. Fully covariant wave functions for octet as well as decuplet baryons are used to calculate form factors and processes like kaon photoproduction. Corresponding results are presented.

Octet and decuplet baryons in a confining and covariant diquark-quark model

We treat baryons as bound states of scalar or axialvector diquarks and a constituent quark which interact through quark exchange. We obtain fully four-dimensional wave functions for both octet and decuplet baryons as solutions of the corresponding Bethe-Salpeter equation. Applications currently under investigation are: electromagnetic and strong form factors and strangeness production processes.

N-quantum approach to quantum field theory at finite T and μ: the NJL model

We extend the N-quantum approach to quantum field theory to finite temperature ( T) and chemical potential ( μ) and apply it to the NJL model. In this approach the Heisenberg fields are expressed using the Haag expansion while temperature and chemical potential are introduced simultaneously through a generalized thermal Bogoliubov transformation. Known mean field results are recovered using only the first term in the Haag expansion. In addition, we find that at finite T and in the broken symmetry phase of the model the mean field approximation can not diagonalize the Hamiltonian. Inclusion of scalar and axial vector diquark channels in the SU(2) f ⊗ SU(3) c version of the model can lead to a lowering of the vacuum energy density. We discuss how to go beyond the mean field approximation by including higher order terms in the Haag expansion.

Octet and decuplet baryons in a covariant and confining diquark-quark model

The baryon octet and decuplet masses and Bethe-Salpeter vertex and wave functions are calculated in the ladder approximation to the quark exchange between a scalar or axialvector diquark and a constituent quark. These functions reflecting full Lorentz covariance are given in terms of an expansion in Gegenbauer polynomials. In the rest frame of the baryon, a complete partial wave decomposition of the Bethe-Salpeter wave function is performed. The confinement of quarks and diquarks is implemented via a parametrization of the corresponding propagators. We also discuss some aspects of the momentum routing in the ladder approximation to the Bethe-Salpeter equation. Numerical results for the octet and decuplet masses with broken flavor SU(3) in the conserved isospin limit are presented.

Diquark confinement in an extended NJL model

In a Nambu-Jona-Lasinio model supplemented with an infrared cutoff in addition to the ultraviolet cutoff we study the issue whether diquarks are confined when the model is extended beyond the rainbow-ladder approximation. The gap equation, obtained in a truncation scheme motivated via a non-trivial quark-gluon vertex function, is solved to determine the constituent quark mass if chiral symmetry is spontaneously broken. In a second step, the Bethe-Salpeter equations for mesons and diquarks beyond the ladder approximation are derived, taking care to preserve Goldstone's theorem in the pion channel. While the obtained masses of pseudo-scalar and vector mesons are only moderately shifted compared to the values in the ladder approximation, we observe that scalar diquarks disappear from the physical spectrum and therefore are confined. For axial-vector diquarks we observe indications that the same mechanism may also work, but the NJL model allows no conclusive answer in this channel.

Heavy baryons in the relativistic quark model

In the framework of the relativistic quasipotential quark model the mass spectrum of baryons with two heavy quarks is calculated. The quasipotentials for interactions of two quarks and of a quark with a scalar and axial vector diquark are evaluated. The bound state masses of baryons with are computed.

Electromagnetic N-Δ transition form factors in a covariant quark-diquark model

The electromagnetic N-$\Delta$ transition form factors are calculated in the framework of a formally covariant constituent diquark model. As a spin-3/2 particle the $\Delta$ is assumed to be a bound state of a quark and an axial-vector diquark. The wave function is obtained from a diquark-quark Salpeter equation with an instantaneous quark exchange potential. The three transition form factors are calculated for momentum transfers squared from the pseudothreshold $(M_\Delta-M_N)^2$ up to $-2 (GeV/c)^2$. The magnetic form factor is in qualitative agreement with experiment. We find very interesting results for the ratios E2/M1 and C2/M1.

Covariant diquark-quark model of the nucleon in the Salpeter approach.

We develop a rather simple, formally covariant quark-diquark model of the nucleon. The nucleon is treated as a bound state of a constituent quark and a diquark interacting via a quark exchange. We include both scalar and axial-vector diquarks. The underlying Bethe-Salpeter equation is transformed into a pair of coupled Salpeter equations. The electromagnetic form factors of the nucleon are calculated in the Mandelstam formalism. We obtain a very good description of all electromagnetic form factors for momentum transfers up to -3 (GeV/c)^2.

Octet and decuplet baryons in the hadronized Nambu-Jona-Lasinio model with proper spin projection

Octet and decuplet baryons are described within the hadronized NJL model as diquark-quark states, which are bound by quark exchange. Including scalar and axial-vector diquark correlations, we project the previously obtained relativistic Faddeev equation in a Poincaré invariant fashion onto good spin, using a static approximation to the exchanged quark. The resulting equations for the spin 1 2 octet and the spin 3 2 decuplet are solved numerically.

Nuclear many-body theory for the study of QCD sum rules in matter.

We discuss the calculation of QCD sum rules for hadrons in matter from the point of view of nuclear many-body theory and treat the sum rule for the rho meson as an example. We describe the factorization approximation that is used to calculate four-quark condensates in vacuum and in matter and discuss the corrections to that approximation in some detail. In the case of the rho meson, we find that corrections to the factorization approximation in matter can vary from about 10 to 40 percent depending upon the model used to describe the nucleon. If the nucleon is considered to be composed of a quark coupled to a scalar (T=0) diquark, the corrections are significant, while, if the quark is coupled to an axial-vector (T=1) diquark, the corrections are small. The physical nucleon may be taken to have equal scalar and axial-vector diquark components. In that case, corrections of about 20 percent are found for the density-dependent part of the vector-isovector polarization tensor. More precise estimates require a more detailed picture of nucleon structure than that considered here. In a previous work we discussed the corrections to the factorization approximate for the nucleon-nucleon correlator evaluated in nuclear matter. The corrections we calculated served to eliminate a problematic density dependence of the four-quark condensates that arose when using the factorization approximation in matter. However, our study provided a successful analysis only when the interpolating field advocated by Ioffe was used. The situation in the case of sum rules for the vector-isovector polarization tensor is subject to fewer uncertainties, since the choice of the current is unique. We find that, while the corrections we calculate for the density dependence of the four-quark condensates are not small, they lead to only very small modifications in the predicted density dependence of the rho mass.

Diquarks in QCD with a linear confinement potential

We explore the diquark-quark picture of the octet and the decuplet of low-lying baryons in QCD with a linear confinement potential. The mass spectra of scalar, pseudoscalar, vector and axial-vector diquarks, transforming like\((\underline {\widetilde3} _f ,\underline {\widetilde3} _c )\) and\((\underline 6 _f ,\underline {\widetilde3} _c )\), are analysed. For scalar, pseudoscalar and vector diquarks we find bound states with massesMS≃MP=1.95 GeV, andMV=2.40 GeV, whereas for axial-vector diquarks no bound states exist. We conclude that low-lying baryons cannot be described by the diquark-quark picture. Our results confirm the three-body structure of low-lying baryons, and lead to an unambiguously fixed spinor structure of three-quark currents of low-lying baryons as proposed by Ioffe, Pascual and Tarrach.

Baryons in the NJL model as solutions of the relativistic Faddeev equation

Abstract The relativistic Faddeev equation for three quarks is solved in the SU(2) f × SU(3) c NJL model to get the nucleon and delta states. We truncate the interacting two-body channels to the scalar and axial vector diquark channels, which are expected to be dominant from the non-relativistic analogy. We find that both channels contribute attractively to the nucleon as well as the delta state, and that the principal mechanism for the mass spitting between the nucleon and the delta in this picture is the interaction in the scalar diquark channel, which is not present in the delta state. We show the dependences of the masses of the nucleon and the delta on the specific form of the interaction lagrangian, and derive restrictions on the possible forms of four-fermi interactions.

Use of the Nambu-Jona-Lasino model in the calculation of the density dependence of four-quark condensates.

Recent works concerning QCD sum rules in nuclear matter have provided a new method for the calculation of the nucleon self-energy in matter. The results of that program depend strongly on assumptions made concerning the density dependence of four-quark condensates. If a factorization scheme is used to express the four-quark condensate values in terms of the two-quark condensates, the (Lorentz) scalar self-energy of the nucleon is small. However, if the four-quark condensates have only a weak density dependence, the nucleon scalar self-energy is large and attractive, and is in accordance with Dirac phenomenology. In this paper our goal is to show how the Nambu--Jona-Lasinio model may be used to calculate the density dependence of four-quark condensates. As an elementary example we calculate some of the contributions to a four-quark condensate containing scalar-isoscalar [ital [bar q]q] pairs. These calculations suggest only a very small modification of the value of the scalar-isoscalar condensate in matter relative to the value obtained in the factorization scheme. However, when we continue our study of the correlator of operators with the quantum numbers of the nucleon, we encounter some new and important terms among the four-quark condensates. These have their origin in an exchange process betweenmore » diquarks in the nucleon and diquarks present in the nucleons of the nuclear medium (nuclear matter). These terms may be taken to represent the effects of diquark condensates'' they are present in nuclear matter. If we use the interpolating field advocated by Ioffe we obtain a correction that eliminates the problematic density dependence of the four-quark condensates described above, if nuclear matter contains a similar amount of scalar ([ital T]=0) diquarks and axial-vector ([ital T]=1) diquarks. We believe that our paper provides increased confidence in the use of QCD sum rules in the study of the properties of hadrons in matter.« less