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. 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.

14 pages, 1 figure

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Cited by in corpus (13)

• Scale-Invariant Hidden Local Symmetry, Topology Change and Dense Baryonic Matter II
• Chiral-scale effective theory including a dilatonic meson
• Scale-Invariant Hidden Local Symmetry, Topology Change and Dense Baryonic Matter
• A pseudo-conformal structure in dense baryonic matter
• Scale-chiral symmetry, $\omega$ meson and dense baryonic matter
• Fractionized Skyrmions in Dense Compact-Star Matter
• Old Wine in a New Bottle: Technidilaton as the 125 GeV Higgs -- Dedicated to the late Professor Yoichiro Nambu
• Nuclear Axial Currents from Scale-Chiral Effective Field Theory
• Compact Star Matter: EoS with New Scaling Law
• The "Folk Theorem" on Effective Field Theory: How Does It Fare in Nuclear Physics?
• Origin of Mass - Horizons Expanding from the Nambu's Theory
• Why {\em Explicit} Strangeness Is Not Relevant In Compact Stars
• Probing the Source of Proton Mass by"Unbreaking" Scale-Chiral Symmetry