High-Energy Physics

粒子物理学为物质在最短距离上提供了一种非常精确的描述：标准模型，一种特殊的量子场论。随着实验积极地寻找标准模型之外的物理线索，特别是在大型强子对撞机上，与理论的详细比较变得越来越重要。量子场可以弱或强相互作用，这一建议将发展新的分析技术来计算这两种状态，并约束引力相互作用。这个提议建立在一个强有力的认识之上：通常存在一个独特的量子场论，与给定的对称性和普遍原理兼容。量子场论诞生于相对论和量子力学的结合，近年来的发展表明，由于这种独特性，从最基本的原理出发是一种非常有效的计算策略。散射振幅的精确计算是粒子物理学的基础：它们描述了碰撞所有可能结果的相对概率。近年来，所谓的on-shell方法通过利用基本原理将复杂的过程分解成更简单的过程，在弱耦合近似中显著提高了精度。该提案将通过引入代数几何中的新数学工具，解决下一代振幅计算的突出挑战，特别是如何粘合子过程。除了弱耦合之外，自举方法已经成功地应用于保形（无标度）理论。这个建议将把它们的应用扩展到更一般的模型中的散射振幅，包括强作用力理论。申请者的小组将在中间能量的弱耦合近似中制定精确的和规则来约束误差。同样的技术将应用于引力子的散射。在目前缺乏一个独特的量子引力预测理论的情况下，限制可能性是很重要的：一个因果理论与爱因斯坦的广义相对论有多大不同？本研究将对标准模型过程的精密计算领域产生直接影响。定量预测可以直接从一般原理中提取出来，这一概念意义深远。它将对许多子领域的实践者理解、使用和教授微观相互作用的方式产生深远而持久的影响。

Particle physics provides an extraordinarily precise description of matter at the shortest of distances: the Standard Model, a particular quantum field theory. As experiments actively search for hints of physics beyond the Standard Model, notably at the Large Hadron Collider, detailed comparison with theory becomes increasingly crucial. Quantum fields can interact weakly or strongly, and this proposal will develop new analytic techniques to calculate in these two regimes, and to constrain gravitational interactions.This proposal builds on a powerful realization: there is often a unique quantum field theory compatible with given symmetries and universal principles. Quantum field theory was born of the union of relativity and quantum mechanics, and developments from recent years have shown that, thanks to this uniqueness, starting from the most basic principles is a very effective strategy for calculations.Precision calculations of scattering amplitudes are fundamental to particle physics: they describe the relative probabilities of all the possible outcomes of a collision. So-called on-shell approaches have dramatically improved precision in recent years, in a weak coupling approximation, by exploiting basic principles to break complicated processes into simpler ones. This proposal will address outstanding challenges for the next generation of amplitude calculations, notably how to glue back subprocesses, by bringing new mathematical tools from algebraic geometry.Beyond weak coupling, bootstrap methods have been successfully applied to conformal (scale-less) theories. This proposal will extend their use to scattering amplitudes in more general models, including the theory of the strong force. The applicant's group will develop exact sum rules to bound errors in the weak coupling approximation at intermediate energies. The same techniques will be applied to scattering of gravitons. In the current absence of a unique predictive theory of quantum gravity, it is important to limit the possibilities: How different from Einstein's general relativity could a causal theory be?This research will have a direct impact on the field of precision calculations of Standard Model processes. The notion that quantitative predictions can be extracted directly from general principles is far-reaching. It will have a profound and long-lasting influence on the way microscopic interactions are understood, used, and taught by practitioners in many subfields.