We study the properties of a system composed of strongly interacting matter with an isospin imbalance, using as an effective description of QCD the two-flavor Linear Sigma Model with quarks. From the one-loop effective potential, including the two light quarks, pions and sigma contributions, and enforcing the restrictions imposed by chiral symmetry, we show that the development of an isospin condensate comes together with the emergence of a Goldstone mode that provides a constraint for the chiral and isospin condensates as a result of a non-trivial mixing between the charged pions and the sigma. We compute the thermodynamical quantities of interest and in particular the sound velocity squared, showing that it presents a maximum for an isospin chemical potential similar to the one reported by lattice QCD results and also with a similar height. Therefore, we attribute the origin of the peak of the sound velocity to the proper treatment of the Goldstone mode and to the non-trivial mixing of the charged pions and sigma in the isospin condensed phase.

中文翻译：

---

关于等旋不平衡强相互作用物质的声速峰值的原点


我们研究了由具有等旋不平衡的强相互作用物质组成的系统的性质，使用夸克的双风味线性 Sigma 模型作为 QCD 的有效描述。从单环有效势，包括两个轻夸克、π 和 σ 贡献，并执行手性对称性施加的限制，我们表明同轴凝聚态的发展与 Goldstone 模式的出现相伴而生，该模式为手性和同轴谐聚态提供了约束，这是带电介子和 σ 之间的非平凡混合的结果。我们计算了感兴趣的热力学量，特别是声速的平方，表明它呈现的同位旋化学势的最大值与晶格 QCD 结果报告的化学势相似，并且高度也相似。因此，我们将声速峰值的来源归因于对 Goldstone 模式的适当处理以及带电介子和 σ 在等旋凝聚相中的非平凡混合。