Resolving the Quenched $g_A$ Puzzle in Nuclei and Nuclear Matter

The long-standing puzzle of the quenched $g_A$ in nuclei – and in dense matter – is shown to have a simple resolution in a scale-symmetric HLS chiral Lagrangian at the Fermi-liquid fixed point. This resolution exposes scale-chiral symmetry, hidden in QCD in the vacuum, emerging in nuclear matter from low density to high compact-star density. It has important implications on “first principles” approaches to nuclear physics, such as the role of multi-body exchange currents in Gamow-Teller matrix elements in nuclei and in neutrinoless double $\beta$ decays for going Beyond the Standard Model.