Pinning Down the Axial-Vector Coupling Constant in Nuclei and Dense Matter

The in-medium property of the axial-vector coupling constant $g_A$ in nuclei and dense baryonic matter, a long standing problem in nuclear physics, is reformulated in terms of the recently constructed scale-invariant hidden local symmetric ($bs$HLS) Lagrangian that encompasses the physics of baryon density ranging from nuclear matter $n_0$ to that of massive compact stars, $\sim 6n_0$. It is shown that unlike the pion decay constant $f_\pi$ that slides with the vacuum change induced by, and dropping with, increasing density, the axial-current constant $g_A$ should remain more or less unaffected by the decrease of chiral condensate in nuclear Gamow-Teller transitions (involving the space component of the axial current) whereas it gets strongly enhanced in axial-charge transitions (involving the time component of the axial current) as density increases. This phenomenon confirms the "chiral filter hypothesis" inferred from the current algebras in 1970's. These phenomena can be taken as a "nuclear physics proof" of Weinberg's folk theorem on quantum effective field theories. The implications of these predictions on giant Gamow-Teller resonances in nuclei and on first-forbidden beta transitions (relevant to nuclear astrophysical processes) are discussed.