The Role of Vector Mesons for Emergent Scale-Chiral Symmetry in Nuclear Interactions

When a light scalar dilaton $\sigma$ and the light-quark vector mesons $V=(\rho,\omega)$ are incorporated into an effective scale-invariant hidden local symmetric (sHLS) Lagrangian, scale symmetry for $\sigma$ and local gauge symmetry for $V$, both invisible in QCD in the vacuum, arise as emergent symmetries at a density above $n_{1/2}\sim 2n_0$, a phenomenon highly relevant for massive compact stars, hitherto unobserved in standard chiral pertubative approaches. What takes place involves a topology change at $n_{1/2}$, and as the density increases beyond, (1) exposes a parity doubling in the nucleon structure, (2) triggers drastic change in the nuclear tensor force and (3) stiffens the nuclear symmetry energy as density exceeds $n_{1/2}$. It results from an intricate interplay between the two hidden symmetries that the $\rho$ meson moves toward the vector manifestation (VM) fixed point where $m_\rho\rightarrow 0$ and the velocity of sound $v_s$ in the dense matter approaches the conformal symmetry value $v_s/c=\sqrt{1/3}$, indicating a presence of an infrared fixed point at which the dilaton mass vanishes.