Anomaly-Induced Quenching of $g_A$ in Nuclear Matter and Impact on Search for Neutrinoless $\beta \beta$ Decay

Abstract

How to disentangle the possible {\it genuine} quenching of $g_A$ caused by scale anomaly of QCD parameterized by the scale-symmetry-breaking quenching factor $q_{ssb}$ from nuclear correlation effects is described. This is done by matching the Fermi-liquid fixed point (FLFP) theory to the ``Extreme Single Particle (shell) Model" (acronym ESPM) in superallowed Gamow-Teller transitions in heavy doubly-magic shell nuclei. The recently experimentally observed indication for $(1-q_{ssb})\ne 0$ -- that one might identify as ``fundamental quenching ({\it FQ})" -- in certain experiments seems to be alarmingly significant. I present arguments how symmetries hidden in the matter-free vacuum can emerge and suppress such {\it FQ} in strong nuclear correlations. How to confirm or refute this observation is discussed in terms of the superallowed Gamow-Teller transition in the doubly-magic nucleus ${}^{100}$Sn and in the spectral shape in the multifold forbidden $\beta$ decay of ${}^{115}$In.

Comments: Title change and extended for invited paper