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Title: In-medium {omega} meson mass and quark condensate in a Nambu-Jona-Lasinio model constrained by recent experimental data

Abstract

We have determined the relation between the in-medium {omega} meson mass and quark condensate in the framework of a Nambu-Jona-Lasinio model constrained by some recent experimental data on the meson properties in nuclei. In addition to the usual four-quark interactions, we have included eight-quark terms in the Lagrangian. The parameters of this model have been determined using the meson properties in the vacuum as well as in the medium. More particularly, we have constrained both the in-medium pion decay constant to the value measured in experiments on deeply bound pionic atoms and the in-medium {omega} meson mass to the experimental value obtained either by the TAPS collaboration or by the E325 experiment at KEK Proton Synchrotron. Our results are compared to several scaling laws and in particular to that of G. E. Brown and M. Rho [(Phys. Rep. 398, 301 (2004)].

Authors:
; ;  [1]
  1. Universite Bordeaux 1, CNRS/IN2P3, Centre d'Etudes Nucleaires de Bordeaux-Gradignan, UMR 5797 Chemin du Solarium, BP120, 33175 Gradignan (France)
Publication Date:
OSTI Identifier:
20995250
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. C, Nuclear Physics; Journal Volume: 75; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevC.75.048201; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
73 NUCLEAR PHYSICS AND RADIATION PHYSICS; BAG MODEL; COLOR MODEL; DECAY; INTERACTIONS; JAPANESE ORGANIZATIONS; LAGRANGIAN FUNCTION; MASS; NUCLEAR MATTER; NUCLEI; OMEGA BARYONS; PIONIC ATOMS; PIONS; PROTONS; QUARK CONDENSATION; QUARKS; SYNCHROTRONS

Citation Formats

Huguet, R., Caillon, J. C., and Labarsouque, J. In-medium {omega} meson mass and quark condensate in a Nambu-Jona-Lasinio model constrained by recent experimental data. United States: N. p., 2007. Web. doi:10.1103/PHYSREVC.75.048201.
Huguet, R., Caillon, J. C., & Labarsouque, J. In-medium {omega} meson mass and quark condensate in a Nambu-Jona-Lasinio model constrained by recent experimental data. United States. doi:10.1103/PHYSREVC.75.048201.
Huguet, R., Caillon, J. C., and Labarsouque, J. Sun . "In-medium {omega} meson mass and quark condensate in a Nambu-Jona-Lasinio model constrained by recent experimental data". United States. doi:10.1103/PHYSREVC.75.048201.
@article{osti_20995250,
title = {In-medium {omega} meson mass and quark condensate in a Nambu-Jona-Lasinio model constrained by recent experimental data},
author = {Huguet, R. and Caillon, J. C. and Labarsouque, J.},
abstractNote = {We have determined the relation between the in-medium {omega} meson mass and quark condensate in the framework of a Nambu-Jona-Lasinio model constrained by some recent experimental data on the meson properties in nuclei. In addition to the usual four-quark interactions, we have included eight-quark terms in the Lagrangian. The parameters of this model have been determined using the meson properties in the vacuum as well as in the medium. More particularly, we have constrained both the in-medium pion decay constant to the value measured in experiments on deeply bound pionic atoms and the in-medium {omega} meson mass to the experimental value obtained either by the TAPS collaboration or by the E325 experiment at KEK Proton Synchrotron. Our results are compared to several scaling laws and in particular to that of G. E. Brown and M. Rho [(Phys. Rep. 398, 301 (2004)].},
doi = {10.1103/PHYSREVC.75.048201},
journal = {Physical Review. C, Nuclear Physics},
number = 4,
volume = 75,
place = {United States},
year = {Sun Apr 15 00:00:00 EDT 2007},
month = {Sun Apr 15 00:00:00 EDT 2007}
}
  • The branching ratios and photon spectra of the rare processes {rho}({omega}) {sup {yields} {pi}0{pi}0{gamma}}, {rho}({omega}) {sup {yields} {eta}{pi}0{gamma}} are calculated in the framework of the standard local quark Nambu-Jona-Lasinio model. Three types of diagrams are considered: the quark box and the pole diagrams with scalar ({sigma}, {alpha}{sub 0}(980)) and vector ({rho}, {omega}) mesons. The obtained estimates for the widths of the processes {rho}({omega}) {sup {yields} {pi}0{pi}0{gamma}} are in satisfactory agreement with existing experimental data. Predictions are made for the widths of the processes {rho}({omega}) {sup {yields} {eta}{pi}0{gamma}}.
  • The dual quark condensate {sigma}{sup (n)} proposed recently as a new order parameter of the spontaneous breaking of the Z{sub 3} symmetry are evaluated by the Polyakov-loop extended Nambu-Jona-Lasinio (PNJL) model, where n are winding numbers. The Polyakov-loop extended Nambu-Jona-Lasinio model well reproduces lattice QCD data on {sigma}{sup (1)} measured very lately. The dual quark condensate {sigma}{sup (n)} at higher temperatures is sensitive to the strength of the vector-type four-quark interaction in the Polyakov-loop extended Nambu-Jona-Lasinio model and hence a good quantity to determine the strength.
  • We discuss inhomogeneous ground states of the Nambu-Jona-Lasinio and quark-meson model within mean-field approximation and their possible existence in the respective phase diagrams. For this purpose we focus on lower-dimensional modulations and point out that known solutions in the 2+1 and 1+1 dimensional (chiral) Gross-Neveu model can be lifted to the to the 3+1 dimensional Nambu-Jona-Lasinio model. This is worked out in detail for one-dimensional modulations and numerical results for the phase diagrams are presented. Focus is put on the critical point and on vanishing temperatures. As an interesting result the first order transition line in the phase diagram ofmore » homogeneous phases gets replaced by an inhomogeneous phase which is bordered by two second order transition lines.« less
  • The Nambu-Jona-Lasinio model with a Polyakov loop is extended to the finite isospin chemical potential case, which is characterized by the simultaneous coupling of the pion condensate, chiral condensate, and Polyakov loop. The pion condensate, chiral condensate, and Polyakov loop as functions of temperature and isospin chemical potential are investigated by minimizing the thermodynamic potential of the system. The resulting (T,{mu}{sub I}) phase diagram is studied with emphasis on the critical point and Polyakov loop dynamics. The tricritical point for the pion superfluidity phase transition is confirmed, and the phase transition for isospin symmetry restoration in the high isospin chemicalmore » potential region perfectly coincides with the crossover phase transition for the Polyakov loop. These results agree with the lattice QCD data.« less
  • We investigate the chiral condensate and the dressed Polyakov loop or dual chiral condensate at finite temperature and density in the two-flavor Nambu-Jona-Lasinio model. The dressed Polyakov loop is regarded as an equivalent order parameter of deconfinement phase transition in a confining theory. We find the behavior of a dressed Polyakov loop in the absence of any confinement mechanism quite interesting. With only quark degrees of freedom present, it still shows an order parameter like behavior. It is found that in the chiral limit, the critical temperature for chiral phase transition coincides with that of the dressed Polyakov loop inmore » the whole (T,{mu}) plane. In the case of explicit chiral symmetry breaking, it is found that the transition temperature for chiral restoration T{sub c}{sup {chi}} is smaller than that of the dressed Polyakov loop T{sub c}{sup D} in the low baryon density region where the transition is a crossover. With the increase of the current quark mass the difference between the two transition temperatures is found to be increasing. However, the two critical temperatures coincide in the high baryon density region where the phase transition is of first order. We give an explanation on the feature of T{sub c}{sup {chi}}=T{sub c}{sup D} in the case of 1st and 2nd order phase transitions, and T{sub c}{sup {chi}}<T{sub c}{sup D} in the case of crossover, and expect this feature is general and can be extended to full QCD theory. Our result might indicate that in the case of crossover, there exists a small region where chiral symmetry is restored, but the color degrees of freedom are still confined.« less