Precise determination of the low energy constants of the chiral Lagrangian using the epsilon-regime of chiral perturbation theory

标准模型面临的主要挑战之一是理解像QCD这样本质上简单的理论是如何在低能量下产生惊人的结构的。原则上，允许我们在QCD中解决这些问题的相干方案的基础是将在不同夸克质量值下进行的点阵QCD模拟与手性摄动理论（χPT）相结合。这个有效的理论是用耦合、低能量常数（LECs）来参数化的，它包含了QCD动力学的所有非摄动信息。lec是关键的兴趣，因为它们提供了QCD的高度非平凡动力学和大量物理可观测物的轻夸克质量依赖之间的独特联系。LECs的确定仍有改进的余地。该项目的主要目标是研究χPT中的不同观察值和功率计数，以精确确定LECS。考虑到lec的通用性，这允许进一步约束它们的值，并且考虑到该方法的通用性，它可以用于所有用标准计算难以确定的lec。

One of the main challenges within the Standard Model is to understand how an intrinsically simple theory like QCD can give rise to the amazing structures observed at low energy. A basis for a coherent scheme that would allow us, in principle, to address these problems in QCD, is to combine Lattice QCD simulations performed at different values of the quark masses with chiral perturbation theory (χPT). This effective theory is parametrized in terms of couplings, low energy constants (LECs), which contain all the non-perturbative information of the QCD dynamics. The LECs are of key interest because they provide the unique link between the highly non-trivial dynamics of QCD and the light quark mass dependence of a plethora of physical observables. There is still room for improvements in the determination of LECs. The main goal of this project is to investigate different observables and power countings within χPT for a precise determination of the LECS. Given the universality of the LECs this allows to further constrain their value and given the generality of the approach it can be used for all the LECs which are poorly determined with standard computations.