Meson mixing effects on the speed of sound in isospin-imbalanced matter

TL;DR

This paper investigates how meson mixing and Goldstone modes in isospin-imbalanced matter affect the speed of sound, revealing a peak that aligns with lattice QCD results and highlighting the role of meson dynamics.

Contribution

It introduces a detailed analysis of meson mixing effects on the speed of sound in isospin-imbalanced matter within the Linear Sigma Model, emphasizing the impact of Goldstone modes.

Findings

A pronounced peak in the speed of sound as a function of isospin chemical potential.

Meson dynamics and Goldstone modes influence the peak's position and width.

The peak's characteristics align with lattice QCD simulations.

Abstract

We explore isospin imbalanced strongly interacting matter within the two-flavor Linear Sigma Model with quarks, an effective model for low-energy QCD. At one loop order, including quark, pion, and sigma fluctuations while respecting chiral symmetry, we find that the formation of an isospin condensate necessarily gives rise to a Goldstone mode. This mode enforces a nontrivial relation between the chiral and isospin condensates through the mixing of charged pions and the sigma field in the condensed phase. From the resulting thermodynamic potential, we compute the speed of sound and observe a pronounced peak as a function of the isospin chemical potential. Although the peak of the speed of sound may be described at tree-level and including only quarks in the analysis, meson dynamics introduces further constraints that influence the position and width of the peak which making it to align well with lattice QCD simulations. Therefore we identify that the shape and position of the peak is a consequence of the Goldstone mode dynamics and of the associated charged pion sigma mixing.