An Effective Field Theory at Finite Density

Abstract

An effective theory to treat the dense nuclear medium by the perturbative expansion method is proposed as a natural extension of the Heavy Baryon Chiral Perturbation Theory (HBChPT). Treating the Fermi momentum scale as a separate scale of the system, we get an improved convergence and the conceptually clear interpretation. We compute the pion decay constant and the pion velocity in the nuclear medium, and find their characters different from what the usual HBChPT predicts. We also obtain the Debye screening scale at the normal nuclear matter density, and the damping scale of the pion wave. Those results indicate that the present theory, albeit its improvement over the HBChPT, has the limitation yet to go over to the medium of about 1.3 times of normal matter density due to the absence of the intrinsic density dependence of the coupling constants. We discuss how we overcome this limitation in terms of the renormalization method.