Studying medium effects with the optimized $\ bdelta $ expansion

Physics Letters B, 1996

The optimized δ-expansion is used to study vacuum polarization effects in the Walecka model. The optimized δ-expansion is a nonperturbative approach for field theoretic models which combines the techniques of perturbation theory and the variational principle. Vacuum effects on self-energies and the energy density of nuclear matter are studied up to O(δ 2). When exchange diagrams are neglected, the traditional Relativistic Hartree Approximation (RHA) results are exactly reproduced and, using the same set of parameters that saturate nuclear matter in the RHA, a new stable, tightly bound state at high density is found.

The European Physical Journal A - Hadrons and Nuclei, 1998

The optimized δ-expansion is a nonperturbative approach for field theoretic models which combines the techniques of perturbation theory and the variational principle. This technique is discussed in the λφ 4 model and then implemented in the Walecka model for the equation of state of nuclear matter. The results obtained with the δ expansion are compared with those obtained with the traditional mean field, relativistic Hartree and Hartree-Fock approximations.

AIP Conference Proceedings, 2004

Medium modification of nucleon properties are studied in the framework of the Linear Sigma Model (LSM). The nucleon is described as a chiral soliton with 3-quarks bounded due to their interactions with sigma and pion fields. Medium effects are introduced through the coupling of the quarks to sigma and omega fields, the strengths of which are determined self-consistently in a Walecka-like model, whose fermionic nucleon mass is calculated in the framework of the LSM. The nucleon properties are presented as functions of the nuclear density.

The European Physical Journal A, 2004

Recently we have proposed a new cutoff scheme for pion loop integrals in the two-pion exchange potential. This method allows for a consistent implementation of constraints from pion-nucleon scattering and has been successfully applied to peripheral nucleon-nucleon partial waves. We now consider low partial waves in the non-perturbative regime, where the regularized Lippmann-Schwinger equation has to be solved in order to generate the bound and scattering states. We observe an improved description of most of the phase shifts when going from next-to-to next-to-next-to-leading order in the chiral expansion. We also find a good description of the deuteron properties. In addition, the new cutoff scheme allows to avoid the presence of unphysical deeply bound states. We discuss the cutoff dependence of the four-nucleon lowenergy constants and show that their numerical values can be understood in terms of resonance saturation. This connects the effective field theory approach to boson exchange phenomenology.

Physical Review C, 1994

We calculate the effective mass of the ω meson in nuclear matter in a relativistic random-phase approximation to the Walecka model. The dressing of the meson propagator is driven by its coupling to particle-hole pairs and nucleon-antinucleon (NN) excitations. We report a reduction in the ω-meson mass of about 170 MeV at nuclear-matter saturation density. This reduction arises from a competition between the density-dependent (particle-hole) dressing of the propagator and vacuum polarization (NN pairs). While densitydependent effects lead to an increase in the mass proportional to the classical plasma frequency, vacuum polarization leads to an even larger reduction caused by the reduced effective nucleon mass in the medium.

Physical Review C, 2016

We study the effect of temperature (T) and baryon density (µ) dependent hadron masses on the thermodynamics of hadronic matter. We use linear scaling rule in terms of constituent quark masses for all hadrons except for light mesons. T and µ dependent constituent quark masses and the light mesons masses are computed using 2+1 flavor Nambu-Jona-Lasinio (NJL) model. We compute the thermodynamical quantities of hadronic matter within excluded volume hadron resonance gas model (EHRG) with these T and µ dependent hadron masses. We confront the thermodynamical quantities with the lattice quantum chromodynamics (LQCD) at µ = 0 GeV. Further, we comment on the effect of T and µ dependent hadron masses on the transport properties near the transition temperature (Tc).

Physical Review D, 2019

A regularization scheme that explicitly separates vacuum contributions from medium effects is applied to a Nambu-Jona-Lasinio model with diquark interactions and in β equilibrium. We perform a comparison of this proposed scheme with the more traditional one, where no separation of vacuum and medium effects is done. Our results point to both qualitative and quantitative important differences between these two methods, in particular regarding the phase structure of the model in the cold and dense nuclear matter case.

An effective theory to treat the dense nuclear medium by the perturbative expansion method is proposed as a natural extension of the Heavy Baryon Chiral Perturbation Theory (HBChPT). Treating the Fermi momentum scale as a separate scale of the system, we get an improved convergence and the conceptually clear interpretation. We compute the pion decay constant and the pion velocity in the nuclear medium, and find their characters different from what the usual HBChPT predicts. We also obtain the Debye screening scale at the normal nuclear matter density, and the damping scale of the pion wave. Those results indicate that the present theory, albeit its improvement over the HBChPT, has the limitation yet to go over to the medium of about 1.3 times of normal matter density due to the absence of the intrinsic density dependence of the coupling constants. We discuss how we overcome this limitation in terms of the renormalization method.

International Journal of Modern Physics E, 2012

Two-loop corrections for the standard Abelian Nambu-Jona-Lasinio model are obtained with the Optimized Perturbation Theory (OPT) method. These contributions improve the usual mean-field and Hartree-Fock results by generating a 1/Nc suppressed term, which only contributes at finite chemical potential. We take the zero temperature limit observing that, within the OPT, chiral symmetry is restored at a higher chemical potential µ, while the resulting equation of state is stiffer than the one obtained when mean-field is applied to the standard version of the model. In order to understand the physical nature of these finite Nc contributions, we perform a numerical analysis to show that the OPT quantum corrections mimic effective repulsive vector-vector interaction contributions. We also derive a simple analytical approximation for the mass gap, accurate at the percent level, matching the mean-field approximation extended by an extra vector channel to OPT. For µ µc the effective vector coupling matching OPT is numerically close (for the Abelian model) to the Fierz-induced Hartree-Fock value G/(2Nc), where G is the scalar coupling, and then increases with µ in a well-determined manner.

Physical Review C, 1995

\simeq \frac{m_{\sigma}(T)}{m_{\sigma}}$ while we argue, using PCAC, that pion mass does not scale within the temperature range involved in our Lagrangian. It is found that the hadron masses and the pion decay constant drop faster with temperature in the dilated chiral quark model than in the conventional linear sigma model that does not take into account the QCD scale anomaly. We attribute the difference in scaling in heat bath to the effect of baryonic medium on thermal properties of the hadrons. Our finding would imply that the AGS experiments (dense {\it and} hot matter) and the RHIC experiments (hot and dilute matter) will ``see" different hadron properties in the hadronization phase.