Scalar Pseudo-Nambu-Goldstone Boson in Nuclei and Dense Nuclear Matter

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. That notion which puts the scalar -- that we shall identify as a dilaton -- on the same footing as the pseudo-scalar 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 (S$chi$PT) to scale chiral perturbation theory, denoted $chi$PT$_sigma$, with {it one infrared mass scale for both symmetries}, with the $sigma$ figuring as a chiral singlet NG mode in non-strange sector. Applied to nuclear dynamics, it is seen to provide possible answers to various hitherto unclarified nuclear phenomena such as the success of one-boson-exchange potentials (OBEP), the large cancellation of strongly attractive scalar potential by 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 $omega$ in dense skyrmion matter, the BPS 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.