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

我们的项目涉及到量子色动力学(QCD)的非微扰方面的研究，量子色动力学是一种被认为描述基本粒子之间强相互作用的场论。特别地，我们考虑了以规范不变的方式在晶格上正则化的理论，其中非微扰计算通过蒙特卡罗模拟是可行的。我们将把注意力集中在与标准模型唯象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的弱哈密顿算符的矩阵元，它们由非微扰QCD贡献所主导。我们计划模拟夸克场的两种不同的紫外线正则化：手征扭转的威尔逊费米子(扭转质量)和手性不变的金斯帕格-威尔逊费米子的重叠实现(对于小体积)。我们还将改进相关的算法技术：使用重叠费米子的有效计算，最初仍处于猝灭近似(即没有海夸克效应)；费米子的非猝灭模拟，在第一阶段仅限于计算成本较低的具有手性扭曲的威尔逊费米子的公式。

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.