Wolfgang Bentz

The stability of nuclear matter in the Nambu–Jona-Lasinio model

Abstract Using the Nambu–Jona-Lasinio model to describe the nucleon as a quark–diquark state, we discuss the stability of nuclear matter in a hybrid model for the ground state at finite nucleon density. It is shown that a simple extension of the model to simulate the effects of confinement leads to a scalar polarizability of the nucleon. This, in turn, leads to a less attractive effective interaction between the nucleons, helping to achieve saturation of the nuclear matter ground state. It is also pointed out that that the same effect naturally leads to a suppression of “Z-graph” contributions with increasing scalar potential.

Ward identity in the many-body system and magnetic moments

Abstract We study the role of the electromagnetic Ward identity in the many-body system. A relativistic framework for density-dependent renormalizations is used. We study the constraints imposed by the Ward identity on the renormalization of the angular momentum g-factor gl and work out the connection with traditionally considered core-polarization and exchange-current processes.

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.

Isovector EMC effect and the NuTeV anomaly

A neutron or proton excess in nuclei leads to an isovector-vector mean field which, through its coupling to the quarks in a bound nucleon, implies a shift in the quark distributions with respect to the Bjorken scaling variable. We show that this result leads to an additional correction to the NuTeV measurement of sin2thetaW. The sign of this correction is largely model independent and acts to reduce their result. Explicit calculation in nuclear matter within a covariant and confining Nambu-Jona-Lasinio model predicts that this vector field correction may account for a substantial fraction of the NuTeV anomaly. We are therefore led to offer a new interpretation of the NuTeV measurement, namely, that it provides further evidence for the medium modification of the bound nucleon wave function.

Spin-dependent structure functions in nuclear matter and the polarized EMC effect

An excellent description of both spin-independent and spin-dependent quark distributions and structure functions has been obtained with a modified Nambu--Jona-Lasinio model, which is free of unphysical thresholds for nucleon decay into quarks--hence incorporating an important aspect of confinement. We utilize this model to investigate nuclear medium modifications to structure functions and find that we are readily able to reproduce both nuclear matter saturation and the experimental F2N(A)/F2N ratio, that is, the European Muon Collaboration (EMC) effect. Applying this framework to determine g1p(A), we find that the ratio g1p(A)/g1p differs significantly from unity, with the quenching caused by the nuclear medium being about twice that of the spin-independent case. This represents an exciting result, which, if confirmed experimentally, will reveal much about the quark structure of nuclear matter.

Faddeev approach to the nucleon in the Nambu-Jona-Lasinio (NJL) model

Abstract The nucleon is studied in the NJL model using the Faddeev equation truncated to the scalar diquark channel. We solve the relativistic Faddeev equation numerically, and compare the results with the static approximation. It is shown that in the original NJL model the coupling constant in the scalar diquark channel is too weak to form a bound state. In order to get about the right nucleon mass, this coupling constant should be about 2 3 of that in the pionic q q channel.

A sigma-omega-quark model to saturate nuclear matter

Abstract A sigma-omega-quark model is investigated to explain the saturation properties of nuclear matter. The quark structure of the nucleon induces a mechanism for saturation by weakening the attraction due to the sigma meson at high density. The boost of the composite system and some center-of-mass corrections are new sources of repulsion and therefore strongly reduce the need for an omega meson.

Solution of the relativistic three quark Faddeev equation in the Nambu-Jona-Lasinio (NJL) model

Abstract The relativistic Faddeev equation for quarks is solved in the NJL model including the axial-vector diquark channel together with the scalar one. It is found that the axial-vector diquark channel contributes significantly to the energy of the nucleon state. We show the region of the effective coupling constants in the scalar and axial-vector diquark channels which gives about the right nucleon mass. In particular, the color current type interaction Lagrangian gives a reasonable nucleon mass.

Isoscalar currents and nuclear magnetic moments

Abstract We investigate meson-exchange current effects on isoscalar nuclear magnetic moments taking a one-boson exchange model. For some cases we find appreciable contributions, though the results are very model dependent. We also discuss the connection between exchange currents and the calculation of magnetic moments in the relativistic σ-ω model.

EMC and polarized EMC effects in nuclei

We determine nuclear structure functions and quark distributions for {sup 7}Li, {sup 11}B, {sup 15}N and {sup 27}Al. For the nucleon bound state we solve the covariant quark-diquark equations in a confining Nambu--Jona-Lasinio model, which yields excellent results for the free nucleon structure functions. The nucleus is described using a relativistic shell model, including mean scalar and vector fields that couple to the quarks in the nucleon. The nuclear structure functions are then obtained as a convolution of the structure function of the bound nucleon with the light-cone nucleon distributions. We find that we are readily able to reproduce the EMC effect in finite nuclei and confirm earlier nuclear matter studies that found a large polarized EMC effect.