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

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.

Figures (1)

• Figure 1: Speed of sound squared $c_s^2$ as a function of $\mu_I/m_\pi$ for two different vacuum quark masses, compared with lattice QCD results from Abbott et al. Abbott2023 and Brandt et al. Brandt2023. The peak structure and its dependence on $m_f$ are clearly visible.