In-medium chiral condensate beyond linear density approximation

Abstract

In-medium chiral perturbation theory is used to calculate the density dependence of the quark condensate $<\bar{q}q>$. The corrections beyond the linear density approximation are obtained by differentiating the interaction contributions to the energy per particle of isospin-symmetric nuclear matter with respect to the pion mass. Our calculation treats systematically the effects from one-pion exchange (with $m_{\pi }$-dependent vertex corrections), iterated $1\pi$-exchange, and irreducible $2\pi$-exchange including intermediate $\Delta (1232)$-isobar excitations, with Pauli-blocking corrections up to three-loop order. We find a strong and non-linear dependence of the ``dropping'' in-medium condensate on the actual value of the pion (or light quark) mass. In the chiral limit, $m_{\pi }=0$, chiral restoration appears to be reached already at about 1.5 times normal nuclear matter density. By contrast, for the physical pion mass, $m_{\pi }=135$MeV, the in-medium condensate stabilizes at about 60% of its vacuum value above that same density. Effects from $2\pi$-exchange with virtual $\Delta (1232)$-isobar excitations turn out to be crucial in generating such pronounced deviations from the linear density approximation above ${\rho }_0$. The hindered tendency towards chiral symmetry restoration provides a justification for using pions and nucleons as effective low-energy degrees of freedom at least up to twice nuclear matter density.

15 pages, 7 figures

References in corpus (15)

• The QCD transition temperature: results with physical masses in the continuum limit
• ππscattering
• Nuclear Force from Lattice QCD
• The transition temperature in QCD
• Peripheral NN-Scattering: Role of Delta-Excitation, Correlated Two-Pion and Vector Meson Exchange
• A microscopic estimate of the nuclear matter compressibility and symmetry energy in relativistic mean-field models
• Chiral Dynamics and Nuclear Matter
• The Stability of Nuclear Matter in the Nambu-Jona-Lasinio Model
• Chiral approach to nuclear matter: Role of two-pion exchange with virtual delta-isobar excitation
• Nucleon mass: from lattice QCD to the chiral limit
• Saturation from nuclear pion dynamics
• Relativistic nuclear energy density functional constrained by low-energy QCD
• Chiral extrapolation of g_A with explicit Delta(1232) degrees of freedom
• Spin-asymmetry energy of nuclear matter
• Nuclear matter in the chiral limit and the in-medium chiral condensate

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