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

TL;DR

This paper proposes a scale chiral perturbation theory incorporating a scalar dilaton as a pseudo-Nambu-Goldstone boson, providing new insights into nuclear phenomena and dense matter by unifying scalar and pseudoscalar mesons within a symmetry framework.

Contribution

It introduces a novel scale chiral perturbation theory that treats the scalar dilaton on equal footing with pseudoscalar mesons, explaining various nuclear phenomena and dense matter properties.

Findings

Explains the success of one-boson-exchange potentials in nuclear physics.

Accounts for the cancellation of scalar and vector potentials in relativistic mean field models.

Provides a framework for understanding hyperon suppression in neutron stars.

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. 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.