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

标准模型中的一个主要挑战是理解像QCD这样本质上简单的理论如何在低能下产生令人惊讶的结构。一个相干方案的基础，将允许我们，在原则上，解决这些问题的QCD，是联合收割机格点QCD模拟进行不同的夸克质量值与手征微扰理论（χPT）。这个有效的理论是参数化的耦合，低能常数（LEC），其中包含所有的非微扰信息的QCD动力学。LEC是关键的兴趣，因为它们提供了独特的联系之间的高度非平凡的动力学QCD和轻夸克质量依赖的大量的物理观测。在确定LEC方面仍有改进的余地。该项目的主要目标是研究不同的可观测量和功率计数在χPT的LECS的精确测定。考虑到LEC的普遍性，这允许进一步约束它们的值，并且考虑到该方法的普遍性，它可以用于用标准计算很难确定的所有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.