Forest Formulas for the LHC

大型强子对撞机的森林公式

• 批准号: MR/Y003829/1
• 负责人: Franz Herzog
• 金额: $ 75.35万
• 依托单位: University of Edinburgh
• 依托单位国家: 英国
• 项目类别: Fellowship
• 财政年份: 2024
• 资助国家: 英国
• 起止时间: 2024 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=MR%2FY003829%2F1
• 关键词: Forest; Formulas; LHC

One of the greatest scientific events of the century is the discovery of the Higgs boson by CERN's Large Hadron Collider (LHC). Yet the LHCs discovery potential has by no means been exhausted as collisions are now happening with an increasing rate at energies never achieved before by mankind. With more and more data being accumulated over the next 15 years we will obtain measurements at unprecedented levels of precision. This data will put stringent new tests on the Standard Model (SM) of particle physics. While the success of the SM is the greatest achievement of particle physics to date, it also poses many mysteries to physicists. For instance, the SM does not explain the observed matter-antimatter asymmetry, or the nature of dark matter and dark energy in the universe. To overcome these problems new models, featuring as exotic ideas as supersymmetry or extra dimensions, have been proposed. So far none of these models could be detected in experiments, but beyond-the-SM (BSM) physics may still be detected at the energy currently explored by the LHC.To distinguish new physics from the SM, theoretical calculations must match the accuracy of the experimental measurements. This poses a tremendous challenge since it is impossible to calculate general observables exactly in quantum field theory. Instead, theoretical physicists resort to what is called the perturbative expansion; this is a systematic way to expand the complicated functions, which describe the scattering rates, in a series in the interaction strength, where each successive term is smaller than the preceding. By calculating enough terms in this expansion one can thus obtain increasingly reliable results. Especially in quantum chromodynamics (QCD), which governs the dynamics of the constituent quarks and gluons of the proton, the convergence of this expansion is relatively slow and in certain cases computations with three or four terms are required. The problem with this approach is that the Feynman diagrams, which appear in the individual terms of this expansion, rapidly increase in both number and complexity. To make matters worse, these Feynman diagrams also contain complicated infrared (IR) and ultraviolet (UV) divergences (singularities) which are of long- and short-distance origin.While the problem of UV divergences has been solved already half a century ago by the procedure of renormalisation, the situation is very different for the IR divergences. Calculating higher-order effects in QCD requires the combination of two separate contributions: real corrections (due to emissions of observable particles) and virtual (loop or quantum) corrections. While it is well known that the divergences of the real emission corrections cancel with those of the virtual corrections, the cancellations only happen after all the different loop and phase-space integrals have been performed.A rigorous approach to renormalisation is given by the Bogoliubov-Parasiuk-Hepp-Zimmermann (BPHZ) scheme also known as the "forest formula", where the term forest refers to sets of nested or disjoint divergent subgraphs. The key idea of this project is to develop and use "generalised forest formulas" for the subtraction of IR divergences. While this proposition is far from trivial, recent breakthroughs which I have made in my recent research have already proven the concept, obtaining a plethora of new results which could not have been achieved by other means. The future potential of this approach is great, as it opens the door for new ways of calculating quantities, which are desperately needed to improve the precision of current theory predictions, such as the 4-loop splitting functions, which govern the energy dependence of partons in the proton, and the 2-loop anomalous dimensions which govern the energy dependence of coupling parameters in the SM EFT, a general model-independent framework to BSM physics.

本世纪最伟大的科学事件之一是欧洲核子研究组织的大型强子对撞机（LHC）发现希格斯玻色子。然而，大型强子对撞机的发现潜力还没有被耗尽，因为碰撞现在发生的速度越来越快，其能量是人类以前从未达到过的。随着未来 15 年积累的数据越来越多，我们将以前所未有的精度获得测量结果。这些数据将对粒子物理学的标准模型（SM）进行严格的新测试。虽然SM的成功是粒子物理学迄今为止最伟大的成就，但它也给物理学家带来了许多谜团。例如，SM 无法解释观察到的物质-反物质不对称性，或者宇宙中暗物质和暗能量的本质。为了克服这些问题，人们提出了新的模型，其特点是超对称或额外维度等奇异的想法。到目前为止，这些模型都无法在实验中检测到，但在大型强子对撞机目前探索的能量下，仍然可以检测到超越SM（BSM）物理。为了区分新物理和SM，理论计算必须与实验测量。这提出了巨大的挑战，因为不可能在量子场论中精确计算一般可观测量。相反，理论物理学家诉诸所谓的微扰展开。这是一种系统地扩展复杂函数的方法，这些函数描述了相互作用强度的一系列散射率，其中每个连续项都小于前面的项。通过在此展开中计算足够的项，我们可以获得越来越可靠的结果。特别是在控制质子夸克和胶子动力学的量子色动力学（QCD）中，这种展开式的收敛相对较慢，在某些情况下需要三项或四项计算。这种方法的问题在于，以这种展开式的各个项出现的费曼图的数量和复杂性都迅速增加。更糟糕的是，这些费曼图还包含复杂的红外 (IR) 和紫外 (UV) 发散（奇点），这些发散源于长距离和短距离。而紫外发散问题在半个世纪前就已经被解决了在重整化过程中，IR 散度的情况非常不同。计算 QCD 中的高阶效应需要结合两个单独的贡献：真实校正（由于可观察粒子的发射）和虚拟（环或量子）校正。虽然众所周知，实际发射校正的分歧与虚拟校正的分歧相抵消，但这种抵消仅在执行了所有不同的循环和相空间积分之后才会发生。Bogoliubov-给出了严格的重整化方法 - Parasiuk-Hepp-Zimmermann (BPHZ) 方案也称为“森林公式”，其中术语森林是指嵌套或不相交发散子图的集合。该项目的关键思想是开发和使用“广义森林公式”来减去 IR 散度。虽然这个命题绝非微不足道，但我最近的研究取得的突破已经证明了这个概念，获得了大量其他方法无法实现的新结果。这种方法的未来潜力是巨大的，因为它为计算数量的新方法打开了大门，这些方法迫切需要提高当前理论预测的精度，例如控制部分子能量依赖性的 4 环分裂函数质子中的能量，以及控制 SM EFT（BSM 物理的通用模型独立框架）中耦合参数的能量依赖性的 2 环反常维度。