Peak of sound velocity, scale symmetry and nuclear force in baryonic matter

Abstract: The sound velocity in homogeneous matter has its fundamental significance as it relates to the stiffness of the equation of state of compact star matter. In this work, we investigate the density evolution of the sound velocity in homogeneous {neutron matter at zero temperature} by using an effective field theory implemented with a conformal compensator -- the nonlinear realization of scale symmetry -- regarded as the source of the lightest scalar meson. We find that the peak of sound velocity emerges naturally in the intermediate density region -- $(1\sim 2.5)n_0$ -- without resorting to any transitions from hadron to exotic configurations or introducing new degrees of freedom. This phenomenon is not found in the Walecka-type models where the sigma meson is included in the linear-type approach, therefore, it is an intrinsic character of the dilaton compensator approach through the matching of QCD trace anomaly, and it connects to the character of the lightest scalar meson. In addition, these observations shed light on how the hidden scale symmetry manifests in nuclear medium from the unitarity limit in dilute matter to dilaton limit in compact star matter.