Manifestation of scale symmetry in nuclear medium

Abstract

This memorial tribute to Mannque Rho focuses on the role of scale symmetry in baryonic matter, especially on its profound influence on the possible resolution of the ``quenched $g_A$" problem in the Gamow-Teller transition of nuclei, the pseudoconformal structure of dense nuclear matter and the origin of the peak of sound velocity of nuclear matter. The discussion is based on the genuine dilaton scenario, anchored on the Crewther-Tunstall infrared fixed point, which provides a unified framework where scale symmetry---broken explicitly by the QCD trace anomaly---can be spontaneously broken, yielding the scalar $f_0(500)$ as a pseudo-Nambu-Goldstone boson. In nuclear medium, this scenario serves as a natural foundation of the Brown-Rho scaling---a relation that has been central to nuclear physics for over three decades. The sound velocity of nuclear matter exhibits a characteristic peak at intermediate densities arising from the kink behavior of the dilaton field, a unique signature of scale symmetry realization that distinguishes the dilaton-compensated effective theory from conventional Walecka-type models. At higher densities, the approach to the dilaton-limit fixed point produces pseudo-conformal behavior with sound velocity $v_s^2 = 1/3$ saturating from below at $n \gtrsim 3n_0$, while the trace of the energy-momentum tensor remains nonzero. The framework also provides a natural resolution of the long-standing ``quenched $g_A$" problem, demonstrating that nuclear correlations, not fundamental quenching, account for the effective axial coupling approaching unity. The continuity from the unitary limit at low density to the dilaton limit at high density suggests a pervasive role for scale symmetry in nuclear dynamics across all density regimes.