We calculate the density-dependent spin-isospin asymmetry energy J(k f ) of nuclear matter in the three-loop approximation of chiral perturbation theory. The interaction contributions to J(k f ) originate from one-pion exchange, iterated one-pion exchange, and irreducible two-pion exchange with no, single, and double virtual ∆-isobar excitation. We find that the approximation to 1π-exchange and iterated 1π-exchange terms (which leads already to a good nuclear matter equation of state by adjusting an emerging contactterm) is spin-isospin stable, since J(k f 0 ) ≃ 24 MeV > 0. The inclusion of the chiral πN ∆-dynamics, necessary in order to guarantee the spin-stability of nuclear matter, keeps this property intact. The corresponding spin-isospin asymmetry energy J(k f ) stays positive even for extreme values of an undetermined short-distance parameter J 5 (whose possible range we estimate from realistic NN-potentials). The largest positive contribution to J(k f ) (a term linear in density) comes from a two-body contact-term with its strength fitted to the empirical nuclear matter saturation point.PACS: 12.38. Bx, 21.65.+f In recent years a novel approach to the nuclear matter problem has emerged. Its key element is a separation of long-and short-distance dynamics and an ordering scheme in powers of small momenta. At nuclear matter saturation density ρ 0 ≃ 0.16 fm −3 the Fermi momentum k f 0 and the pion mass m π are comparable scales (k f 0 ≃ 2m π ), and therefore pions must be included as explicit degrees of freedom in the description of the nuclear many-body dynamics. The contributions to the energy per particleĒ(k f ) of isospin-symmetric (spin-saturated) nuclear matter as they originate from chiral pion-nucleon dynamics have been computed up to threeloop order in Refs. [1,2]. Both calculations are able to reproduce the empirical saturation point of nuclear matter by adjusting one single parameter (either a contact-coupling g 0 + g 1 ≃ 3.23 [1] or a cutoff scale Λ ≃ 0.65 GeV [2]) related to unresolved short-distance dynamics.1 The basic mechanism for saturation in this approach is a repulsive contribution to the energy per particlē E(k f ) generated by Pauli-blocking in second order (iterated) pion-exchange. As outlined in Sec. 2.5 of Ref.[2] this mechanism becomes particularly transparent by taking the chiral limit m π = 0. In that case the interaction contributions toĒ(k f ) are completely summarized by an attractive k 3 f -term and a repulsive k 4 f -term where the parameter-free prediction for the coefficient of the latter is very close to the one extracted from a realistic nuclear matter equation of state.In a recent work [3] we have extended the chiral approach to nuclear matter by including systematically the effects from 2π-exchange with virtual ∆(1232)-isobar excitation. The physical motivation for such an extension is threefold. First, the spin-isospin-3/2 ∆(1232)-resonance 1 Fitting a cutoff scale, as done in Ref.[2], must be viewed as a short-term intermediate step before an eventual full ...
