Properties of Nuclear Matter in Cutoff Field Theory and the Low-Energy Effective Lagrangian in the Hartree Approximation

et al. 2000

Int. J. Mod. Phys. E

Based on quantum hadrodynamics with a finite cutoff, the effective masses of vector mesons (ω,ρ) in nuclear medium are calculated. We use a low-energy effective Lagrangian which is obtained by integrating high-energy quantum fluctuations. Although we use an artificial cutoff, the cutoff-dependence can be removed order by order. It is also found that the effective ρ-meson mass [Formula: see text] decreases as the density increases. The rate of the decrease becomes smaller at high density. As a result, at the normal density, [Formula: see text] is 0.85~0.92.

Section: Effective Lagrangian In the Hartree Approximationmentioning

confidence: 97%

“…Referring to our previous work [30,31], we introduce a low-energy effective Lagrangian in the σ-ω model using the Hartree approximation.…”

Section: Effective Lagrangian In the Hartree Approximationmentioning

confidence: 99%

Section: Effective Lagrangian In the Hartree Approximationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Effective Vector Meson Masses in a Cutoff Field Theory

Sakamoto

Nakai

et al. 2000

Int. J. Mod. Phys. E

“…In the recent paper [8], we have studied the nuclear matter properties in details using the cutoff field theory of Cohen and show that the properties of nuclear matter may be somewhat different from those described in the ordinary renormalization procedures. In the same paper, the cutoff field theory of the nuclear matter is reformulated in the framework of the renormalization group methods [9][10] [11] and the fifth and sixth order terms of σ-meson self-interactions in the effective Lagrangian are shown to be important in the cutoff field theory.…”

Section: Introductionmentioning

confidence: 99%

Meson-Nucleon Vertex Corrections in the Cutoff Field Theory and Tensor Coupling

Progress of Theoretical Physics

Koide

Noda

et al. 1998

Self Cite

At zero-density, meson-nucleon vertex corrections to vacuum polarization are studied in the σ-ω model with the cutoff. It is shown that the properties of the vertex corrections to vacuum polarization are somewhat different from those described by the ordinary renormalization procedures when the cutoff is small ( < 5GeV). The low-energy effective Lagrangian is constructed in the framework of the renormalization group method. The weak tensor and derivative couplings of meson-nucleon interactions may be needed in the lowenergy effective theory of mesons and nucleons.

Non-Perturbative Renormalization Group Equations in Quantum Hadrodynamics

Progress of Theoretical Physics

Nakai

Hasegawa

et al. 2000

Self Cite

Quantum hadrodynamics are studied with non-perturbative renormalization group equations. It is shown that the contributions of one-loop diagrams are important for the effective potential, since effective couplings of lower-order interactions in the effective potential are only slightly affected by quantum effects at low energy. The relation between the localpotential approximation (LPA) and the traditional Hartree approximation is discussed. The LPA includes the contribution of the Fock term to the nucleon self-energy, the contribution in the random phase approximation to the meson self-energy, and vertex corrections in part, as well as the Hartree contribution to the effective potential. §1. IntroductionIn the past quarter century, nuclei and nuclear matter have been studied in the framework of quantum hadrodynamics (QHD). 1), 2) The meson mean-field theory of nuclear matter 1) has produced successful results to account for the saturation properties at normal nuclear density. Following these successes, many studies and modifications have been made of relativistic nuclear models. One of these modifications is the inclusion of vacuum fluctuation effects, which cause divergences in physical quantities when they are naively calculated. Chin 3) estimated the vacuum fluctuation effects in the Hartree approximation by using a renormalization procedure, and found that vacuum fluctuation effects make the incompressibility of nuclear matter smaller and closer to the empirical value than in the original Walecka model.Although the relation between QHD and the underlying fundamental theory, i.e., QCD, is not clear, it is natural that QHD is not valid at very high energy. From this point of view, a cutoff or a form factor should be introduced into the theory of QHD. One may introduce such a cutoff 4) or form factor 5) to avoid the instability of the meson propagators in a random phase approximation (RPA). 6) Cohen 7) introduced a four-dimensional cutoff into the relativistic Hartree approximations (RHA) and found that the vacuum energy contributions may be somewhat different from those in the ordinary renormalization procedures, if the cutoff is not too large.One troublesome problem in the use of a finite cutoff is that physical results depend on the value of the cutoff and the shape of the regulator which are introduced into the theory by hand. It is difficult to determine a suitable value of the cutoff and * )