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, $n_{1\mathrm{/}2}$, 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 $n_{1\mathrm{/}2}\sim 2n_0$ 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 $M\simeq 2.01M_{\odot }$ and the radius $R\simeq 12.0$ km and (4) the sound velocity $v_s^2\mathrm{/}{c}^2\simeq 1\mathrm{/}3$ 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.