Nuclear chiral dynamics and thermodynamics

Abstract

This presentation reviews an approach to nuclear many-body systems based on the spontaneously broken chiral symmetry of low-energy QCD. In the low-energy limit, for energies and momenta small compared to a characteristic symmetry breaking scale of order 1 GeV, QCD is realized as an effective field theory of Goldstone bosons (pions) coupled to heavy fermionic sources (nucleons). Nuclear forces at long and intermediate distance scales result from a systematic hierarchy of one-and two-pion exchange processes in combination with Pauli blocking effects in the nuclear medium. Short distance dynamics, not resolved at the wavelengths corresponding to typical nuclear Fermi momenta, are introduced as contact interactions between nucleons. Apart from a set of low-energy constants associated with these contact terms, the parameters of this theory are entirely determined by pion properties and low-energy pion-nucleon scattering observables. This framework (in-medium chiral perturbation theory) can provide a realistic description of both isospin-symmetric nuclear matter and neutron matter, with emphasis on the isospin-dependence determined by the underlying chiral NN interaction. The importance of three-body forces is emphasized, and the role of explicit ∆(1232)-isobar degrees of freedom is investigated in detail. Nuclear chiral thermodynamics is developed and a calculation of the nuclear phase diagram is performed. This includes a successful description of the first-order phase transition from a nuclear Fermi liquid to an interacting Fermi gas and the coexistence of these phases below a critical temperature T c . Density functional methods for finite nuclei based on this approach are also discussed. Effective interactions, their density dependence and connections to Landau Fermi liquid theory are outlined. Finally, the density and temperature dependence of the chiral (quark) condensate is investigated.

Functional renormalization group studies of nuclear and neutron matter

“…It simultaneously provides the foundation for systematic nuclear structure studies of few-and many-body systems. Current state-of-the-art potentials 12 have progressed to chiral order N 4 LO (fifth order in Q/Λ) and achieved still further substantial improvements in comparison with empirical NN two-body data, including peripheral phase shifts and np polarization observables [58,59]. Convergence has been successfully demonstrated by investigating dominant contributions of order N 5 LO [60].…”

“…Various applications of in-medium chiral perturbation theory have been reported in recent years (see [12,13] and refs. therein).…”

“…This is the starting point for a systematic approach to nuclear many-body dynamics and thermodynamics at densities and temperatures well within the hadronic, "confined" phase of QCD [12,13] 4 .…”

Asymmetric nuclear matter based on chiral two- and three-nucleon interactions

“…For symmetric matter it was found that low-momentum NN plus 3N interactions are capable to predict realistic saturation properties, with 3N forces fit only to few-body data [7], whereas neutron matter was found to be perturbative [8]. In subsequent studies, symmetric matter and neutron matter were also investigated based on chiral EFT interactions within the self-consistent Green's function framework [9,10], using coupled-cluster theory [11,12], with in-medium chiral perturbation theory [13] and in many-body perturbation theory [14]. Furthermore, the development of novel local chiral NN forces opened the way to first Quantum Monte Carlo studies of neutron matter based on chiral EFT interactions [15][16][17][18].…”

Dileptons and Chiral Symmetry Restoration

“…One finds pc 0.3 GeV which is comparable to that of cold nuclear matter at twice saturation density. Of course, one should keep in mind that the chiral condensate at T pc is still at about half of its vacuum value, which, again is in the vicinity of recent estimates in cold nuclear matter at twice nuclear saturation density [13]. Figure 1: Dilepton spectra in heavy-ion collisions from HADES at SIS [3] (left), CERES [5] and NA60 [6] at SPS (middle panels) and STAR [7] at RHIC (right panel), compared to theoretical calculations with QGP and hadronic emission using the same model for the in-medium ρ spectral function [9,10,11,12].…”