Scale-Chiral Symmetry, Proton Mass and Sound Velocity in Compact-Star Matter

With a light dilaton $sigma$ and the light-quark vector mesons $V=(rho,omega)$ incorporated into an effective scale-invariant hidden local symmetric Lagrangian, scale-chiral symmetry -- hidden in QCD -- arises at a high density, $n_{1/2}$, as an emergent symmetry, a phenomenon absent in standard chiral perturbative approaches but highly relevant for massive compact stars. What takes place as the density increases beyond $n_{1/2}sim 2n_0$ in compressed baryonic matter is (1) a topology change from skyrmions to half-skyrmions, (2) parity doubling in the nucleon structure, (3) the maximum neutron star mass $Msimeq 2.01 M_{odot}$ and the radius $Rsimeq 12.0$ km and (4) the sound velocity $v_s^2/c^2simeq 1/3$ due to the vector manifestation (VM) fixed point of $rho$ and a walking dilaton condensate, which is intricately connected to the source of the proton mass.