High precision calculations in quantum field theory

接下来的十年对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，这些数据将使我们能够进入一个全新的能量域，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、超对称等。另一方面，低能实验精度的提高使粒子相互作用标准模型的基本参数的精确测定成为可能，并在探索超越标准模型的新物理方面具有竞争力。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，预测的高精度就变得必不可少了。该项目的主要目标是计算从非相对论性阈值到超相对论性苏达科夫极限等广泛量子场论问题中的高阶微扰修正，这对当前和未来的实验具有重要的现象学意义。这尤其包括对电子-正电子散射的电弱辐射修正，这是电子-正电子对撞机的“标准烛光”，对顶-反顶阈值产生和底铵态特性的强耦合辐射修正，夸克和正电子超细分裂的高阶分析。结果的可能现象学应用包括精确测定重夸克质量和强耦合常数。这些问题的难度要求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。更深入地理解和发展这些概念以及在凝聚态物理中可能的应用场论方法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.