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. 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.We are grateful for valuable correspondences with Rod Crewther and Lewis Tunstall on their approach to the QCD dilaton and for discussions with Koichi Yamawaki on the technidilaton for Higgs. Part of this paper was written when two of the authors (H. K. L. and M. R.) were visiting the Theory Group of RISP, IBS, for which we are grateful to Youngman Kim for support. The work of W. G. P. is supported by the Rare Isotope Science Project of Institute for Basic Science funded by Ministry of Science, ICT and Future Planning and National Research Foundation of Korea (2013M7A1A1075764)