Chiral approach to nuclear matter: Role of two-pion exchange with   virtual delta-isobar excitation
  We extend a recent three-loop calculation of nuclear matter in chiral perturbation theory by including the effects from two-pion exchange with single and double virtual $\Delta(1232)$-isobar excitation. Regularization dependent short-range contributions from pion-loops are encoded in a few NN-contact coupling constants. The empirical saturation point of isospin-symmetric nuclear matter, $\bar E_0 = -16 $MeV, $\rho_0 = 0.16 $fm$^{-3}$, can be well reproduced by adjusting the strength of a two-body term linear in density (and weakening an emerging three-body term quadratic in density). The nuclear matter compressibility comes out as $K = 304 $MeV. The real single-particle potential $U(p,k_{f0})$ is substantially improved by the inclusion of the chiral $\pi N\Delta$-dynamics: it grows now monotonically with the nucleon momentum $p$. The effective nucleon mass at the Fermi surface takes on a realistic value of $M^*(k_{f0})=0.88M$. As a consequence of these features, the critical temperature of the liquid-gas phase transition gets lowered to the value $T_c \simeq 15 $MeV. In this work we continue the complex-valued single-particle potential $U(p,k_f)+i W(p,k_f)$ into the region above the Fermi surface $p>k_f$. The effects of $2\pi$-exchange with virtual $\Delta$-excitation on the nuclear energy density functional are also investigated. The effective nucleon mass associated with the kinetic energy density is $\widetilde M^*(\rho_0)= 0.64M$. Furthermore, we find that the isospin properties of nuclear matter get significantly improved by including the chiral $\pi N\Delta$-dynamics. 
S. Fritsch, N. Kaiser, and W. Weise