High Precision Calculations in Quantum Field Theory

量子场论的高精度计算

• 批准号: SAPIN-2022-00020
• 负责人: Penin, Alexander
• 金额: $ 7.21万
• 依托单位: University of Alberta
• 依托单位国家: 加拿大
• 项目类别: Subatomic Physics Envelope - Individual
• 财政年份: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=762548
• 关键词: Precision; Calculations; Quantum; Field; Theory

Over the last few years the Large Hadron Collider (LHC) has transformed from a raw discovery into a high-precision machine. Despite many expectations no direct signal of new phenomena such as the extra space dimensions, supersymmetry, low-scale gravity etc. has been detected so far. Thus the "new physics" is likely to show up only as a tiny deviation of the experimental data from the theoretical predictions based on the standard model of particle interactions. At the same time the increasing accuracy of the low-energy experiments allows for a very accurate determination of the fundamental parameters of particle physics and becomes competitive in probing  physics beyond the standard model. Hence, the theoretical analysis which is able to provide the required precision becomes ultimately important.  The main aim 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 Regge and Sudakov limit, which are of primary phenomenological importance for current and future experiments. One of the most interesting  field of the proposed research is related to the Higgs boson physics program at the LHC. It includes the perturbative analysis of  two main channels for the production of the Higgs boson or a pair of the Higgs bosons via gluon and electroweak gauge boson fusion. During the last two decades the methods and techniques of the perturbative quantum field theory reached an unprecedented level. The next-to-next-to-next-to-leading results have been obtained in quantum chromodynamics  for a number of the key processes such as Drell-Yan and the Higgs boson production at the LHC and the top quark-antiquark pair threshold production at a future linear collider. However, many of the pending problems  are still beyond the reach of available techniques for a direct calculation or go beyond any finite order of perturbation theory. These problems require a development of the 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, asymptotic expansions, etc. Deeper understanding and development of these concepts are also among the aims of the project. The use of the ideas inherited from quantum field theory has become one of the main trends in the modern condensed matter physics. Such concepts as Majorana fermions, magnetic monopoles, supersymmetry etc., which are yet to be discovered at fundamental level in particle physics, are effectively realized in various condensed matter systems. This gives a significant boost to the application of the quantum field theory methods to condensed matter. I plan to continue the study of physical phenomena at the interface between the quantum fields and condensed matter and to develop and apply the advanced perturbative methods in this context.

在过去的几年里，大型强子对撞机（LHC）已经从一个原始的发现转变为一个高精度的机器。尽管有许多期望，但迄今为止还没有发现新现象的直接信号，如额外的空间维度，超对称性，低尺度引力等。因此，“新物理学”很可能只表现为实验数据与基于粒子相互作用标准模型的理论预测之间的微小偏差。与此同时，低能实验的精度不断提高，使得粒子物理学的基本参数可以非常精确地确定，并在标准模型之外的探测物理学方面具有竞争力。因此，能够提供所需精度的理论分析变得至关重要。 该项目的主要目的是计算从非相对论阈值到超相对论Regge和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。其中一个最有趣的研究领域与LHC的希格斯玻色子物理计划有关。它包括通过胶子和电弱规范玻色子融合产生希格斯玻色子或一对希格斯玻色子的两个主要通道的微扰分析。在过去的二十年中，微扰量子场论的方法和技术达到了前所未有的水平。在量子色动力学中，对于LHC上的Drell-Yan和Higgs玻色子的产生以及未来直线对撞机上的顶夸克-反夸克对阈值产生等关键过程，已经获得了仅次于领先的结果。然而，许多悬而未决的问题仍然超出了现有的技术，直接计算或超越任何有限阶微扰理论。这些问题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，渐近展开等。从量子场论中继承下来的思想已经成为现代凝聚态物理的主要趋势之一。马约拉纳费米子、磁单极子、超对称等概念，这些在粒子物理学的基础水平上还没有被发现，在各种凝聚态系统中有效地实现了。这对量子场论方法在凝聚态物质中的应用起到了重要的推动作用。我计划继续研究量子场和凝聚态物质之间界面的物理现象，并在此背景下发展和应用先进的微扰方法。