Constraints on nuclear matter properties from QCD susceptibilities

We establish the interrelation between the QCD scalar response of the nuclear medium and its response to a scalar probe coupled to nucleons, such as the scalar meson responsible for the nuclear binding. The relation that we derive applies at the nucleonic as well as at the nuclear levels. Non trivial consequences follow. In particular it opens the possibility of relating medium effects in the scalar meson exchange or three-body forces of nuclear physics to QCD lattice studies of the nucleon massComment: Submitted to EPJ

Pions in the nuclear medium

We discuss various aspects of pion physics in the nuclear medium. We first study s-wave pion-nucleus interaction in connection with chiral symmetry restoration and quark condensate in the nuclear medium. We then adress the question of p-wave pion-nucleus interaction and collective pionic modes in nuclei and draw the consequences for in medium $\pi\pi$ correlations especially in the scalar-isoscalar channel. We finally discuss the modification of the rho meson mass spectrum at finite density and/or temperature in connection with relativistic heavy ion collisions.Comment: 13 pages, latex, 8 figures eps (talk given at the Workshop, MESON'96, Cracow, Poland, 14 May 96

Two-pion production processes, chiral symmetry and NN interaction in the medium

We study the two-pion propagator in the nuclear medium. This quantity appears in the $\pi-\pi$ T-matrix and we show that it also enters the QCD scalar susceptibility. The medium effects on this propagator are due to the influence of the individual nucleon response to a scalar field through their pion clouds. This response is appreciably increased by the nuclear environment. It produces an important convergence effect between the scalar and pseudoscalar susceptibilities, reflecting the reshaping of the scalar strengh observed in $2\pi$ production experiments. While a large modification of the $\sigma$ propagator follows, due to its coupling to two pion states, we show that the NN potential remains instead unaffected.Comment: 14 pages, 4 figures, submitted to EPJ

In-medium modification of the isovector pion-nucleon amplitude

We study the in-medium modification of the isovector pi N amplitude using a non-linear representation of the sigma model but keeping the scalar degree of freedom. We check that our result does not depend on the representation. We discuss the connection with other approaches based on chiral perturbation theory.Comment: 7 page

Nuclear matter saturation in a relativistic chiral theory and QCD susceptibilities

We study a chiral relativistic theory of nuclear matter aimed at the desciption of both the binding and saturation properties and the QCD properties, quark condensate and QCD susceptibilities. For this purpose the nucleon scalar response of the quark-meson coupling model is introduced in the linear sigma model. The consequences for the nuclear and the QCD scalar susceptibilities are discussed.Comment: 9 pages, 3 figures, sumitted to Physical Review

QCD susceptibilities and nuclear matter saturation in a chiral theory: inclusion of pion loops

We derive the equation of state of symmetric nuclear matter in a relativistic theory with $\sigma$ and $\omega$ exchange. We take a chiral version of this model which insures all the chiral constraints. Going beyond the mean field approach we introduce the effects of the pion loops. For the parameters of the model, in order to fix those linked to pion exchange, we exploit the most recent information on the short-range part of the spin-isospin interaction. For those linked to the scalar meson exchange we make use of an analysis of lattice results on the nucleon mass evolution with the quark mass. With these inputs we are able reach a correct description of the saturation properties. From the equation of state of symmetric nuclear matter we alsoderive the density dependence of the quark condensate and of the QCD susceptibilities

Chiral symmetry, scalar field and confinement : from nucleon structure to nuclear matter

We discuss the relevance of the scalar modes appearing in chiral theories with spontaneous symmetry breaking such as the NJL model for nuclear matter studies. We show that it depends on the relative role of chiral symmetry breaking and confinement in the nucleon mass origin. It is only in the case of a mixed origin that nuclear matter can be stable and reach saturation. We describe models of nucleon structure where this balance is achieved. We show how chiral constarints and confinement modify the QCD sum rules for the mass evolution in nuclear matter.Comment: talk given by G. Chanfray at the Chiral10 WORKSHOP, Valencia (Spain), June 21-24, 201

From QCD to nuclear matter saturation

We discuss a relativistic chiral theory of nuclear matter with $\sigma$ and $\omega$ exchange using a formulation of the $\sigma$ model in which all the chiral constraints are automatically fulfilled. We establish a relation between the nuclear response to the scalar field and the QCD one which includes the nucleonic parts. It allows a comparison between nuclear and QCD information. Going beyond the mean field approach we introduce the effects of the pion loops supplemented by the short-range interaction. The corresponding Landau-Migdal parameters are taken from spin-isospin physics results. The parameters linked to the scalar meson exchange are extracted from lattice QCD results. These inputs lead to a reasonable description of the saturation properties, illustrating the link between QCD and nuclear physics. We also derive from the corresponding equation of state the density dependence of the quark condensate and of the QCD susceptibilities.Comment: Talk given by M. Ericson at the Yukawa International Seminar (YKIS) 2006 "New frontiers in QCD", Kyoto, Japo

Fluctuations of the quark densities in nuclei

We study the static scalar susceptibility of the nuclear medium, i.e., the change of the quark condensate for a small modification of the quark mass. In the linear sigma model it is linked to the in-medium sigma propagator. At ordinary nuclear densities, when chiral symmetry is spontaneously broken, the scalar susceptibility is distinct from the pseudoscalar one, which is linked to the fluctuations of the quark pseudoscalar density. We show that the pseudoscalar one, which is large in the vacuum, owing to the smallness of the pion mass, follows the density evolution of the quark condensate and thus decreases. The scalar one instead increases due to the mixing with the softer modes of the nucleon-hole excitations. At normal nuclear matter density the two susceptibilities become much closer, a partial chiral symmetry restoration effect as they become equal when the full restoration is achieved.Comment: 9 pages, 1 figure, submitted to Phys. Rev.

Relativistic Chiral Theory of Nuclear Matter and QCD Constraints

We present a relativistic chiral theory of nuclear matter which includes the effect of confinement. Nuclear binding is obtained with a chiral invariant scalar background field associated with the radial fluctuations of the chiral condensate Nuclear matter stability is ensured once the scalar response of the nucleon depending on the quark confinement mechanism is properly incorporated. All the parameters are fixed or constrained by hadron phenomenology and lattice data. A good description of nuclear saturation is reached, which includes the effect of in-medium pion loops. Asymmetry properties of nuclear matter are also well described once the full rho meson exchange and Fock terms are included.Comment: Talk given by G. Chanfray at PANIC 08, Eilat (Israel), november 10-14, 200