From Nuclear Matter with Quenched $g_A$ to Compact-Star Matter with a Signal for Emergent Hidden Scale Symmetry

Abstract

An ``unorthodox" idea is developed that the long-standing mystery in nuclear physics of the effective axial-current coupling constant in nuclei, $g_A^{\rm eff}\approx 1$, could be interpreted in terms of an emerging hidden scale symmetry in dense compact-star matter. Arguments are presented using an effective field theory anchored on a renormalization-group approach to interacting baryons on the Fermi surface coupled with hidden symmetric heavy mesonic degrees of freedom that enables one to go beyond Weinberg's nuclear effective field theory involving nucleon and pion fields only, referred hereon to as $\chi$EFT$_\pi$. Both hidden local and scale symmetries, the former involving the vector mesons $\rho$ and $\omega$ and the latter the hidden scalar meson, a dilaton $\hat{\sigma}$ (i.e., $f_0(500)$), play the crucial role. Going beyond the density regime applicable to normal nuclear matter $n_0$, the notion of ``hadron-quark continuity HQC)" is brought in via the skyrmion structure of the nucleon argued to be valid in QCD at large $N_c$ limit and the large $N^\prime$ limit of the Grassmannian model $G/H= [O(N^\prime)/O(N^\prime-p) \times O(p)]$ where $N^\prime=4$ and $p=2$ for hidden local symmetry and the IR fixed point in QCD for $N_f \leq 3$ involving ``genuine/QCD-conformal dilaton" for hidden scale symmetry. The connection between the quenched $g_A$ and the sound speed $v^2_{s}/c^2\approx 1/3$ inside dense compact stars could be interpreted as a signal for emergent ``pseudo-conformal" symmetry.