The Quenched ${g_A}$ Puzzle in Nuclei & Nuclear Matter and "Pseudo-Conformality" in QCD

Abstract

The long-standing puzzle of the quenched $g_A$ in nuclei is shown to have an extremely simple resolution in a renormalization-group (RG) treatment of a hidden local symmetric (HLS) and scale-symmetric (HSS) chiral Lagrangian. It is shown that the Landau-Migdal fixed-point approximation in nuclear matter (or $V_{lowk}$ in finite nuclei) in RG approach to strong correlations of fermionic hadrons on the Fermi surface {\it exactly} reproduces the superallowed Gamow-Teller transitions in the ``Extreme Single-Particle (shell-)Model (ESPM)" in doubly-magic closed shell nuclei. One arrives at the quenching factor $q\approx 0.78$ giving the quenched $g_A^{\rm eff} \approx 1$. 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 weak axial-current matrix elements in nuclei and in neutrinoless double $β$ decays for going Beyond the Standard Model. This resolution could put in serious doubt the most recent improved measurement of the superallowed Gamow-Teller transition in the doubly-magic closed shell nucleus $^{100}$Sn which if confirmed would require a ``{\it fundamental quenching}" $q_{ssb}\sim 1/2$.