Nicht-perturbative Analyse von Effekten der starken Wechselwirkung, durch numerische Simulationen auf dem Gitter

我们的项目是关于量子色动学（QCD）的非微扰方面的研究，量子色动学是一种被认为描述基本粒子之间强相互作用的场论。特别是，我们认为规范不变的方式在晶格上，非微扰计算是可行的，通过蒙特卡罗模拟的理论正规化。我们将把注意力集中在与标准模型的唯象学相关的量的理论评估上，例如手征微扰理论的低能常数和有效弱哈密顿算符的矩阵元，这些都是由非微扰QCD贡献主导的。我们计划模拟两种不同的夸克场的紫外调节：手征扭曲的威尔逊费米子（扭曲质量）和手征不变的Ginsparg-Wilson费米子的重叠实现（小体积）。我们还将改进相关的算法技术：重叠费米子的有效计算，最初仍然在淬火近似（即没有海夸克效应）;费米子的非淬火模拟，在第一阶段仅限于计算成本较低的手征扭曲威尔逊费米子配方。

Our project is concerned with the investigation of non-perturbative aspects of Quantum ChromoDynamics (QCD), the field theory that is believed to describe strong interaction between elementary particles. In particular, we consider the theory regularised in a gauge invariant way on the lattice, where non-perturbative computations are feasible by means of Monte Carlo simulations. We will focus our attention on the theoretical evaluation of quantities relevant for the phenomenology of the Standard Model, such as Low Energy Constants of Chiral Perturbation Theory and matrix elements of the effective weak Hamiltonian operator, which are dominated by non-perturbative QCD contributions. We plan to simulate two different ultraviolet regularisations of the quark fields: chirally twisted Wilson fermions (twisted mass) and the overlap realization of chirally invariant Ginsparg - Wilson fermions (for small volumes). We also are going to improve algorithmic techniques relevant for: efficient computations with overlap fermions, initially still in the quenched approximation (i.e. without sea quark effects); unquenched simulations of fermions, in a first stage limited to the computationally less expensive formulation with chirally twisted Wilson fermions.