Chiral Dynamics and Nuclear Matter

We calculate the equation of state of isospin-symmetric nuclear matter in the threeloop approximation of chiral perturbation theory. The contributions to the energy per particle Ē(kf ) from oneand two-pion exchange diagrams are ordered in powers of the Fermi momentum kf (modulo functions of kf/mπ). It is demonstrated that, already at orderO(k4 f ), two-pion exchange produces realistic nuclear binding. The underlying saturation mechanism is surprisingly simple (in the chiral limit), namely the combination of an attractive k f -term and a repulsive k f -term. The empirical saturation point and the nuclear compressibility K ≃ 250MeV are well reproduced at order O(k5 f ) with a momentum cut-off of Λ ≃ 0.65GeV which parametrizes short-range dynamics. No further short-distance terms are required in our calculation of nuclear matter. In the same framework we calculate the density-dependent asymmetry energy and find A0 ≃ 34MeV at the saturation point, in good agreement with the empirical value. The pure neutron matter equation of state is also in fair qualitative agreement with sophisticated many-body calculations and a resummation result of effective field theory, but only for low neutron densities ρn < 0.25 fm . PACS: 12.38.Bx, 21.65.+f