Scalar pseudo-Nambu-Goldstone boson in nuclei and dense nuclear matter

Abstract

The notion that the scalar listed as f(0)(500) in the particle data booklet is a pseudo-Nambu-Goldstone (NG) boson of spontaneously broken scale symmetry, explicitly broken by a small departure from an infrared fixed point, is explored in nuclear dynamics. This notion-which puts the scalar (which we shall identify as the "dilaton") on the same footing as the pseudoscalar pseudo-NG bosons, i.e., octet pi, while providing a simple explanation for the Delta I = 1/2 rule for kaon decay-generalizes the standard chiral perturbation theory (chi PT) to "scale chiral perturbation theory," denoted chi PT sigma, with one infrared mass scale for both symmetries, with the sigma figuring as a chiral singlet NG mode in the nonstrange sector. Applied to nuclear dynamics, it is seen to provide answers to various hitherto unclarified nuclear phenomena, such as the success of one-boson-exchange potentials, the large cancellation of a strongly attractive scalar potential by a strongly repulsive vector potential in relativistic mean-field theory of nuclear systems and in-medium QCD sum rules, the interplay of the dilaton and the vector meson. in dense Skyrmion matter, the Bogomol'nyi-Prasad-Sommerfeld Skyrmion structure of nuclei accounting for small binding energies of medium-heavy nuclei, and the suppression of hyperon degrees of freedom in compact-star matter.