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A Bottom-Up EFT Approach To Superdense Baryonic Matter

Mannque Rho

Abstract

How to arrive at the densest matter in massive compact stars starting from Walecka's linear $ω$-$σ$ mean-field model is described in a series of arguments anchored on hidden local symmetry, hidden scale symmetry and emergent parity-doublet symmetry. I follow the bottom-up approach from chiral symmetry with pions, coupled to hidden local and scale symmetry degrees of freedom. Exploiting the renormalization-group treatment à la Shankar and Polchinski of the fermionic interactions on the Fermi sphere, leading to Landau-Migdal Fermi-liquid, one obtains a sort of generalized ``Density Functional" that allows via a topology change hadrons transform to quarks without phase changes at the center of massive stars. The highly dense matter is ``pseudo-conformal" with the sound velocity $v_{pcs}^2/c^2\approx 1/3$ but the trace of the energy-momentum tensor is not equal to zero, hence the matter is non-conformal.

A Bottom-Up EFT Approach To Superdense Baryonic Matter

Abstract

How to arrive at the densest matter in massive compact stars starting from Walecka's linear - mean-field model is described in a series of arguments anchored on hidden local symmetry, hidden scale symmetry and emergent parity-doublet symmetry. I follow the bottom-up approach from chiral symmetry with pions, coupled to hidden local and scale symmetry degrees of freedom. Exploiting the renormalization-group treatment à la Shankar and Polchinski of the fermionic interactions on the Fermi sphere, leading to Landau-Migdal Fermi-liquid, one obtains a sort of generalized ``Density Functional" that allows via a topology change hadrons transform to quarks without phase changes at the center of massive stars. The highly dense matter is ``pseudo-conformal" with the sound velocity but the trace of the energy-momentum tensor is not equal to zero, hence the matter is non-conformal.

Paper Structure

This paper contains 1 section, 3 equations, 2 figures.

Table of Contents

  1. I would like to acknowledge sharing the initial ideas with Hyun Kyu Lee and Won-Gi Paeng on the role of the "hidden" interplay of the $\omega$ and the dilaton $\sigma_d$ in highly dense matter.

Figures (2)

  • Figure 1: Top: Sound velocity $v_{pcs}$ predicted in G$n$EFT for $n_{HQ}=2.5 n_0$. Middle & Bottom: Sound velocities (bottom) predicted in an RMF calculation holt with $M(M_\odot))$ vs. $R$ as inputs.
  • Figure 2: Left panel: For $n_{1/2}=4n_0$, the unitarity bound $v_s^2/c^2=1$ is violated. A rough estimate gives the maximum star mass $M_{\rm max} \sim 2.3 M_\odot$. Right panel: Density dependence of the polytropic index in neutron matter for $n_{1/2}\approx 2.5 n_0$