How and How Much is $g_A$ {\it Fundamentally} Quenched in Nuclei?

The superallowed Gamow-Teller transition in the doubly-magic-shell nucleus ${}^{100}$Sn and the high resolution spectral shape analysis in the fourth-forbidden nonunique transition in ${}^{115}$In indicate as much as $\sim 40\mathrm{\%}$ {\it fundamental} quenching in the axial-current coupling constant $g_A$ in nuclei. This can be attributed to an effect of the trace anomaly in QCD “emerging” in nuclear medium. If confirmed, this would signal a major revamping to do in nuclear interactions consistent with chiral-scale symmetry in nuclear medium and a big impact on $0\nu$ and $\nu \nu$ double $\beta$ decays for BSM. I present an argument that such a big anomaly-induced quenching is incompatible with how hidden scale symmetry manifests in nuclear medium, A possible means to resolve this issue is discussed in terms of hidden scale symmetry permeating in baryonic matter from normal nuclear matter to massive compact-star matter.