Color-magnetic Interaction Research Articles

Quark correlation functions in the proton

The colour-magnetic interaction of QCD with a smearing function found from the fit to the λ-π splitting is strong enough to support a bound state of a singlet ϱ−π pair. We examine the possibility that this interaction leads to short-range quark-quark correlations in light baryons thereby providing the dynamical mechanism for a quark-diquark picture of the proton. In particular, we show that the correlation function of a singlet diquark in the proton is strongly enhanced at the origin (compared to that for the triplet diquark) with the correlation radiusr0, a typical cut-off radius in the spin interaction. The Fourier transform of the correlation function, which is related to the dependence on the momentum transfer of the structure functions in inclusive electron-proton scattering, may provide quite fundamental information on the diquark structure of the proton.

Energy Properties of Strange Quark Matter Studied in Constituent Quark Model

We study energy properties of strange quark matter (SQM) in an approach based on the constituent quark model. In treating the infinite matter, SQM is modeled on a cubic lattice composed of the 1s-closed shell (Q.) clusters, by extending a cluster-theoretical approach previously made for finite strange quark systems of Q.-clusters. The energy per baryon of this SQM monotonically increases as the inter-Qs distance decreases (the density of Q.-clusters as well as the average baryon number density increases). This means that Q.-clusters do not fuse to the Fermi-gas like SQM and favor to be far apart from each other. The mechanism causing such tendency is the following; the repulsive contributions to the inter-Qs energy coming from the kinetic energy and the color magnetic interaction overwhelm the attractive ones from the color electric interaction and, except for the internal energy of Qs, the contributions from a confinement potential play no essential role. The energy of SQM per baryon can never be less than that of a single Q. which is higher by about 400 ~500 MeV than the nucleon mass. Therefore the appearance of the absolutely stable SQM is unlikely in this model. Saturation property of SQM and surface effects are also discussed.

Test of a chromomagnetic model for hadron mass differences.

An oversimplified model consisting of the QCD color-magnetic interaction has been used previously by Silvestre-Brac and others to compare the masses of exotic and normal hadrons. We show that the model can give qualitatively wrong answers when applied to systems of normal hadrons.

Does color-magnetic interaction induce short-range diquark correlations in the proton?

Color-magnetic interaction with a smearing function found from the fit to the ρ-π splitting is strong enough to support a bound state of a single $$q\bar q$$ pair. We present some piloting calculations in order to illustrate the eigenenergy dependence on the cutoff parameter for different choices of the smearing function. In the threequark system the spin-spin interaction can lead to the existence of the short-range correlations in each1 S o qq subsystem, thereby providing the dynamical mechanism for the quark-diquark picture of the proton.

Spin-dependent forces and electromagnetic structure of the nucleon.

The spin-dependent forces, which can arise from either nonperturbative instanton effects or perturbative color magnetic interactions, cause the difference between u-quark and d-quark spatial distributions inside the nucleon. Considering this SU(6) symmetry-breaking effect, the elastic electromagnetic nucleon form factors and static magnetic moments of octet baryons can be well reproduced in the center-of-mass (c.m.) bag model. The same spin force effects on the deep inelastic polarized structure functions are also discussed.

NUCLEAR MATTER STABILITY IN A SOLITON MODEL FOR FINITE NUCLEI

A relativistic band structure method for the computation of the electronic structure of atomic clusters is adapter to the Friedberg–Lee nontopological soliton model. Thus, finite nuclei can be studied in the soliton model. As a verification of our method, we calculated the equation of state of nuclear matter. In order to achieve nuclear matter stability, we added the colour magnetic interaction for an inhomogeneous dielectric medium as well as a phenomenological residual interaction to the soliton model. Both modifications are examined in detail. Nuclear matter stability near the empirical ground state density and binding energy has been achieved.

Nucleon and isobar properties in a relativistic Hartree–Fock calculation with vector Richardson potential and various radial forms for scalar mass terms

Mean-field models of the nucleon (N) and the delta (Δ) are established with the two-quark vector Richardson potential along with various prescriptions for a running quark mass (single particle) in the Dirac–Hartree–Fock formalism. The N–Δ splitting is obtained from colour magnetic interaction and the results for gA and the magnetic moment are discussed. An effective density dependent one-body potential U(ρ) for quarks at a given density ρ inside the nucleon is derived. Asymptotic freedom and confinement properties are built-in in U(ρ) and the model dependence is restricted to the intermediate densities.

Dynamical properties and flux tubes of the Friedberg-Lee model

A new non-polynomial parametrization for the dielectric function of the Friedberg-Lee model is suggested to enforce the confinement of dynamical gluons. The authors investigated flux tube solutions of this model and show how divergences of the colour magnetic quark interaction can be avoided. As effective models for confinement, they contrast the Friedberg-Lee model and Abelian Higgs models. They point out pathological properties of the Friedberg-Lee model: (i) the lack of confinement of high-frequency gluons and (ii) sensitivity of the scalar field dynamics to unphysical vector fields in the non-perturbative vacuum, sigma = sigma V. These problems can be cured only by requiring that all derivatives of the dielectric function kappa ( sigma ) vanish in the non-perturbative vacuum.

Quark-meson model for nuclear force.

Within a quark-meson model of nuclear force with relativistic effects, taking into account the small component of Dirac spinor, the wave function of the relative motion for deuteron and the N-N effective interaction are calculated. The numerical results show that the small component of Dirac spinor is a significant quantity; the small component and the relevant color magnetic interaction directly cause the short-range soft repulsive core of nuclear force. The calculated effective potential and the NN-scattering phase shifts are in reasonable agreement with the experimental data.

Tensor polarization of the elastice−2H scattering and the scaling behavior of six-quark dynamics

Tensor polarization, ${t}_{20}$, of elastic electron-deuteron scattering is calculated with the resonating group method applied to the six-quark system. We stress the role of baryon size for short-range nuclear correlations, such as the short-range repulsion due to the color magnetic interaction, through the six-quark dynamics. Correct sizes of the delta-nucleon mass splitting and the binding energy of the deuteron are the restrictions imposed on the model Hamiltonian for each different choice of the three-quark cluster size b. An interesting scaling behavior for ${t}_{20}$ is observed with regard to the momentum transfer q and b, for different models of the medium-range attractive force. An asymptotic equation predicted by the perturbative quantum chromodynamics, i.e., ${\mathrm{lim}}_{\mathrm{q}\ensuremath{\rightarrow}\mathrm{\ensuremath{\infty}}}$${\mathrm{t}}_{20}$(q)=const, is examined within the present framework, and the momentum transfer for this condition turns out to be quite large, q=4--6 GeV/c. Magnetic effects are seen to be important at large q.

Interaction between two baryons and the six quark model

The 3S, 1S and P wave phase shifts of the nucleon-nucleon interaction are calculated in the six quark model using the resonating group method. For large distances the model is supplemented by π, σ, ϱ and ω-meson exchange. The role of the orbital [42] r symmetry for the short range repulsion is studied. It is shown that at short distances the orbital [42] r symmetry plays an important role which is even enlarged by the colour magnetic interaction. The [42] r symmetry enforces the short range repulsion by a node which it requests at short distances. The mechanism is complicated by the fact, that the orbital [6] r symmetry is also admixed. We show that for meson exchanges which mediate the long range behaviour we can now use the SU 3 flavour ratios of the meson-nucleon coupling constants even for the ω-nucleon coupling. For the ω-meson one had to use in the OBEP's an ω-N coupling constant twice to three times as large as predicted by SU 3 flavour to describe the short range repulsion. We also calculated the nucleon-hyperon interaction and describe the NΛ-scattering in agreement with the data. The model is also applied to study the EMC effect.

Hyperon-nucleon and hyperon-hyperon interaction in a quark model

The non-relativistic quark cluster model is employed to describe the two-baryon systems including hyperons such as Λ, Σ and Ξ. Qualitative discussions about the role of the Pauli principle for quarks and the color magnetic interaction in the baryon-baryon scattering are given. Results of the resonating group method (RGM) calculation show a repulsive interaction at short distances in most of the two-baryon systems with strangeness S = −1 and −2. There appears, however, a sharp resonance in the 1S 0ΛΛ scattering at E = 26.3 MeV, which may correspond to the di-hyperon state.

One-gluon-exchange effects on semileptonic decay of baryon octet

We study one-gluon-exchange (OGE) effects ongA/gV of weak semileptonic decay processes of theSU(3) baryon octet. We especially investigate the systematic behavior of OGE effects on all the possible decay processes and search for better overall agreements between theory and experiment. We adopt the MIT bag model to describe quarks confined in a baryon. We also use a formulation of the perturbative QCD in which gluon field is also confined in the bag. Our calculations respect the boundary conditions which achieve the confinement of each field within the bag. The magnitudes of our corrections togA/gV have a variation of 1 ∼30% depending on the decay, processes. They have process-dependence quite different from that of the uncorrected values ofgA/gV primarily governed by theSU(6) symmetry. These OGE effects ongA/gV reflectSU(6) asymmetric spin-spin correlation between quarks due to the color magnetic interactions. Especially, the OGE corrections togA/gV are very important in the processes,\(\Sigma ^ - \to n + l^ - + \bar v_l ,\Sigma ^ - \to p + l^ - + \bar v_l \) and\(\Xi ^ - \to \Xi ^0 + e^ - + \bar v_e \). Consequently, we clarify that the OGE effects can sizably improve theoretical values ofgA/gV in favor of overall agreements with the present experimental data of semileptonic decays of the baryon octet, at least, in the MIT bag model.

Vacuum condensates in the bag model

The consequences of having quark and gluon condensates inside a MIT bag are investigated. We show that one naturally expects a state dependent bag constant and a colour-magnetic interaction term ∼ R 2. This gives the possibility of having a small strong coupling constant α s inside the bag.

Short-range part of the NN interaction: Lowest-order relativistic corrections to equivalent local potentials from quark exchange kernels

The full Breit hamiltonian, including the Darwin term and relativistic kinetic-energy correction, has been used to construct resonating group kernels in analytic form for the six-quark NN system. The nonlocal kernels have been converted to equivalent local potentials using the WKB approximation based on their Wigner transforms. The equivalent local potentials have been confirmed to be rather insensitive to a choice of parameters and to be fairly accurate by comparing with the phase shifts and the wave functions obtained with the RGM equation. The results indicate the importance of the Darwin term. The term leads to a large reduction of the strong repulsive cores given by the color magnetic interaction and makes the resulting potentials less repulsive than those which neglect this term. The relative importance of the various components in the Breit interaction and of the quark-gluon exchange diagrams is made clear.

Hadron spectroscopy in a flux-tube quark model

Color-magnetic interactions (one-gluon exchange) are incorporated into a semirelativistic quark model and the spectra of ground states and orbital and radial excitations of light mesons, light baryons, charmonium, and $b$-quarkonium are calculated by treating the magnetic splitting exactly by variational methods. The $\ensuremath{\pi}\ensuremath{-}\ensuremath{\rho}$ splitting is fit and the $N\ensuremath{-}\ensuremath{\Delta}$ splitting is predicted in excellent agreement with experiment. In general, spin-spin and tensor splittings among light mesons and light baryons are calculated in good agreement with experiment. The splittings in heavy-meson spectroscopy are also predicted accurately, including the $P$-wave states of charmonium and $b$-quarkonium. Some problems and limitations of the quark-model description of the light mesons and baryons are emphasized. Spin-orbit splittings in the light mesons and $P$-wave baryon multiplets are calculated, but a unified understanding of the systematics is not obtained. Radial excitations in the meson and baryon systems are generally in error by 100-150 MeV, and the systematics are not understood.

Multiquark colour-hyperfine spectra in the bag model: a survey with the P-matrix formalism

The masses of S-wave q 2 q 2 , q 4 q and q 6 multiquark states have been calculated in the M.I.T. bag model after taking proper account of flavour symmetry violations in the single-gluon-exchange magnetic contribution. Mixing induced by the flavour dependence of the colour-magnetic interaction strengths raises some degeneracies and inverts a few levels but does not otherwise greatly affect the masses. However, the mixing does in a few cases result in very substantial changes in the eigenfunctions. These effects are surveyed and the masses and dissociation couplings for the most important states are examined using the P-matrix formalism.

The di-hyperon state in the quark cluster model

The di-hyperon state (DH) predicted by Jaffe in the MIT bag model is studied in the non-relativistic quark cluster model. The resonating group method is applied to the ΛΛ, NΞ and ΣΣ coupled channels problem. No stable bound state is found below the lowest ΛΛ threshold but a sharp resonance with spin-parity 0 + is predicted just below the NΞ threshold. The structure of the state is similar to that of the flavour SU 3 singlet state and the attractive nature of the color magnetic interaction in this state is responsible for the appearance of the resonance. The difference between the present model and the bag model which predicted a strongly bound state is attributed to the difference in the mechanism of confinement for these two models.

The quark model and the nature of the repulsive core of the nucleon-nucleon interaction

The nature of the repulsive core of the nucleon-nucleon interaction is studied in the quark model. The resonating group equation for nucleon-nucleon scattering is solved with the colour Fermi-Breit interaction including further a linear or quadratic confinement potential. It is shown that the colour magnetic interaction which is adjusted to the Δ-nucleon mass splitting favours the [42] orbital symmetry and disfavours the completely symmetric orbital state [6]. For the important [42] orbital symmetry the relative S wave function between the two nucleons has to have a node. In the framework of the resonating group method including the NN, ΔΔ and the hidden colour (CC) channels it is shown that this node produces a 3S and 1S phase shift which is identical to a hard core phase shift with a hard core radius r 0 between 0.3 and 0.6 fm depending on the assumed root mean square radius of the quark part of the nucleon.

Possible color instabilities in abnormal quark matter

When the spatial wave function of a multiquark system is completely antisymmetric, the color-magnetic interaction energy may become attractive or may vanish. Under certain circumstances, this may cause a color-magnetic or color-electric collapse in the abnormal quark matter of singly occupied single-particle orbital states.