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

我们的项目涉及量子色动力学（QCD）的非微扰方面的研究，这种场论被认为描述了基本粒子之间的强相互作用。特别是，我们考虑在晶格上以规范不变的方式正则化的理论，其中通过蒙特卡罗模拟的方式进行非微扰计算是可行的。我们将重点关注与标准模型现象学相关的量的理论评估，例如手性微扰理论的低能量常数和有效弱哈密顿算子的矩阵元素，这些量以非微扰 QCD 贡献为主。我们计划模拟夸克场的两种不同的紫外线正则化：手性扭曲威尔逊费米子（扭曲质量）和手性不变的金斯帕格-威尔逊费米子（小体积）的重叠实现。我们还将改进与以下相关的算法技术：使用重叠费米子进行高效计算，最初仍处于淬灭近似状态（即没有海夸克效应）；费米子的未淬火模拟，在第一阶段仅限于计算成本较低的手性扭曲威尔逊费米子公式。

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.