Constraining the nonanalytic terms in the isospin-asymmetry expansion of nuclear equation of state

The nuclear symmetry energy, defined as the difference of the energy per particle between the pure neutron matter and the symmetric nuclear matter at a fixed density, is crucial for understanding the properties of neutron-rich nuclei and neutron stars. The expansion of the nuclear symmetry energy in even powers of the isospin asymmetry has recently been shown to breakdown in beyond-mean-field-theory calculations of the nuclear equation of state. In this talk we will describe a new finite difference method to extract the fourth- and sixth-order regular and logarithmic contributions to the nuclear symmetry energy with microscopic chiral two- and three-body forces. We find that in general the expansion coefficients of the nonanalytic logarithm terms are larger in magnitude than those of the corresponding regular terms (even-power) for the energy from the second-order perturbation calculation. But overall, the normal terms give larger contributions to the ground state energy. The high-order terms are important to describe the proton fraction in the beta-equilibrium nuclear matter. Different chiral potentials produce different values of those coefficients, which results in uncertainties of the tendency of the proton fraction at the high-density region.