How the axial coupling constant $g_A$ in nuclear Gamow-Teller transitions described in shell model gets “quenched” to a universal constant close to 1 can be explained by nuclear correlations in Fermi-liquid fixed-point theory using a scale-symmetric chiral Lagrangian supplemented with hidden local symmetric vector mesons. Contrary to what one might naively suspect—and has been discussed in some circles—there is no fundamental quenching at nuclear matter density due to QCD condensates. When the density of many-body systems treated with the same Lagrangian increases beyond the density $n=n_{1/2}\gtrsim 2n_0$ (where $n_0$ is the normal nuclear matter density) at which skyrmions representing baryons fractionize to half-skyrmions, with the $\rho$ meson driven toward the vector manifestation fixed point and a scalar meson $\sigma$ driven to the dilaton-limit fixed point with the nucleons parity-doubled, the dense matter supports the “pseudoconformal” sound velocity for $n\gtrsim n_{1/2}$, while the trace of the energy momentum tensor remains nonvanishing. A plausible interpretation is that this signals the emergence of scale symmetry not explicitly present or hidden in QCD in the vacuum. The fundamental constant $g_A$, unaffected by QCD condensates for $n<n_{1/2}$, does go to 1 as the dilaton-limit fixed point is approached before arriving at chiral restoration, but it is not directly related to the “quenched $g_A$” in nuclei which can be explained as a Fermi-liquid fixed point quantity. The mechanism that produces a precocious pseudoconformal sound velocity is expected to impact on the tidal deformability $\mathrm{\Lambda }$ in gravitational waves from coalescing neutron stars.

• Received 25 April 2018

DOI:https://doi.org/10.1103/PhysRevC.98.044318