Lattice measurements provide adequate information to fix the parameters of long-distance effective field theories in Euclidean time. Using such a theory, we examine the analytic continuation of long-distance correlation functions of composite operators at finite temperature from Euclidean to Minkowski space–time. We show through an explicit computation that the analytic continuation of the pion correlation function is possible and gives rise to nontrivial effects. Among them is the possibility, supported by lattice computations of Euclidean correlators, that long distance excitations can be understood in terms of (very massive) pions even at temperatures higher than the QCD crossover temperature.

中文翻译：

---

使用有效理论来自晶格的实时暖π介子

晶格测量提供了足够的信息来确定欧几里得时间长距离有效场论的参数。使用这样的理论，我们研究了从欧几里得到闵可夫斯基时空的有限温度下复合算子的长距离相关函数的解析延拓。我们通过显式计算表明，π介子相关函数的解析延拓是可能的，并且会产生非平凡的影响。其中之一是欧几里得相关器的晶格计算支持的可能性，即使在高于 QCD 交叉温度的温度下，长距离激发也可以用（非常大的）介子来理解。