High precision calculations in quantum field theory

接下来的十年对于我们理解基本粒子和力的基本结构至关重要。大型强子对撞机（LHC）已经在收集数据，这些数据将使人们进入一个全新的能量领域，并可能在不久的将来发现主要的新现象，如额外的空间维度，超对称性，另一方面，提高低-能量实验使得非常精确地确定粒子相互作用标准模型的基本参数成为可能，并且在探测方面具有竞争力超越标准模型的新物理学在大多数情况下，新物理学表现为与基于标准模型的理论预测的微小偏差。因此，预测的高精度成为强制性的。该项目的主要目标是计算从非相对论阈值到超相对论Sudakov极限的广泛一类量子场论问题的高阶微扰修正，这些问题对当前和未来的实验具有重要的唯象学意义。这特别包括对电子-正电子散射的电弱辐射修正，这是电子-正电子对撞机的"标准蜡烛“，对顶-反顶阈值产生和底态性质的强耦合辐射修正，夸克偶素和正电子偶素超精细分裂的高阶分析。这些结果在唯象学上的应用包括重夸克质量和强耦合常数的精确测定。这些问题的难度需要开发新的理论和计算工具，这些工具与量子场论的基本概念密切相关，如有效场论方法，重整化群等，这些概念的深入理解和发展以及凝聚态物理学中场论方法的可能应用也是该项目的目标之一。

The following decade is crucial for our understanding of the fundamental structure of elementary particles and forces. Large Hadron Collider (LHC) is already collecting data which will give access to a completely new energy domain and could in a nearest future uncover principally new phenomena such as the extra space dimensions, supersymmetry, etc. On the other hand increasing accuracy of the low-energy experiments makes possible a very accurate determination of the fundamental parameters of the standard model of particle interactions and becomes competitive in probing new physics beyond the standard model. In most cases the new physics shows up as a tiny deviation from the theoretical predictions based on the standard model. Thus the high precision of the predictions becomes mandatory. The main goal of the project is the calculation of the high order perturbative corrections in a wide class of the quantum field theory problems ranging from nonrelativistic threshold to ultrarelativistic Sudakov limit, which are of primary phenomenological importance for current and future experiments. This includes in particular the electroweak radiative corrections to the electron-positron scattering, which is the ``standard candle'' for electron-positron colliders, the strong coupling radiative corrections to the top-antitop threshold production and to the properties of the bottomonium states, high order analysis of quarkonium and positronium hyperfine splitting. Possible phenomenological applications of the results include precise determination of the heavy quark masses and strong coupling constant. The difficulty of the problems requires developing new theoretical and computational tools which are closely related to the fundamental concepts of the quantum field theory such as the effective field theory approach, renormalization group, etc. Deeper understanding and development of these concepts and possible application of the field theory methods in condensed matter physics are also among the goals of the project.