Forest Formulas for the LHC

大型强子对撞机的森林公式

• 批准号: MR/S03479X/1
• 负责人: Franz Herzog
• 金额: $ 87.71万
• 依托单位: University of Edinburgh
• 依托单位国家: 英国
• 项目类别: Fellowship
• 财政年份: 2020
• 资助国家: 英国
• 起止时间: 2020 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=MR%2FS03479X%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 at energies never achieved before by mankind. With more and more data being accumulated over the next 15 years we will obtain measurements at previously unreached levels of precision. This data will put stringent new tests on the prevalent 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 abundances 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 physics may yet be hiding 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 still impossible to calculate general observables exactly in quantum field theory (the theoretical framework upon which the SM stands). 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. To calculate the higher order effects in QCD requires the calculation 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 establish and use a "generalised forest formula" for the subtraction of the troublesome IR divergences. While this proposition is far from trivial, a breakthrough which I have made in my recent research now gives strong evidence for its correctness. The future potential of this approach is great as it promises an in-principle general solution for calculating scattering rates of an arbitrary number of final-state particles and arbitrary orders in the perturbative expansion. One important objective of the proposed research is to implement this idea in a dedicated code-library and apply it in the calculations of higher-order QCD corrections of key importance for the LHC; such as the production of two and three jets at the respective 4th and 3rd order in the perturbative expansion.

本世纪最伟大的科学事件之一是欧洲核子研究中心的大型强子对撞机（LHC）发现了希格斯玻色子。然而，大型强子对撞机的发现潜力还远远没有耗尽，因为现在发生的碰撞的能量是人类从未达到的。随着未来15年积累的数据越来越多，我们将获得以前未达到的精度水平的测量结果。这些数据将对粒子物理学中流行的标准模型（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不能解释观测到的物质-反物质不对称，也不能解释宇宙中暗物质和暗能量的丰度。为了克服这些问题，人们提出了一些新的模型，这些模型具有超对称或额外维度等奇异的概念。到目前为止，这些模型都没有在实验中被检测到，但超越sm的物理可能隐藏在LHC目前探索的能量中。为了将新物理学与SM区分开来，理论计算必须与实验测量的精度相匹配。这提出了一个巨大的挑战，因为在量子场论（SM所依据的理论框架）中仍然不可能精确地计算一般的可观测值。相反，理论物理学家求助于所谓的微扰膨胀；这是一种系统地展开描述散射率的复杂函数的方法，在相互作用强度的一系列中，其中每个连续项都小于前一个。通过在这个展开式中计算足够多的项，就可以得到越来越可靠的结果。特别是在量子色动力学（QCD）中，它控制着质子的组成夸克和胶子的动力学，这种膨胀的收敛相对较慢，在某些情况下需要用三到四项进行计算。这种方法的问题是，费曼图出现在这个扩展的单个术语中，在数量和复杂性上都迅速增加。更糟糕的是，这些费曼图还包含了复杂的红外（IR）和紫外（UV）发散（奇点），它们有长距离和短距离的起源。虽然紫外散度的问题在半个世纪前就已经通过重整化过程解决了，但红外散度的情况却大不相同。为了计算QCD中的高阶效应，需要计算两个单独的贡献：真实修正（由于可观测粒子的发射）和虚拟修正（环路或量子）。虽然众所周知，实发射校正的散度与虚发射校正的散度相互抵消，但只有在执行了所有不同的环路和相空间积分后才会发生这种抵消。bogoliubov - parasiukk - hepp - zimmermann （BPHZ）方案给出了一种严格的重正规化方法，也称为“森林公式”，其中森林指的是嵌套或不相交发散子图的集合。这个项目的关键思想是建立和使用一个“广义森林公式”来减去麻烦的红外散度。虽然这个命题远非微不足道，但我在最近的研究中取得的一个突破现在为其正确性提供了强有力的证据。这种方法的未来潜力是巨大的，因为它为计算微扰膨胀中任意数量的最终态粒子和任意阶数的散射率提供了原则上的一般解决方案。提出的研究的一个重要目标是在专用代码库中实现这一思想，并将其应用于对大型强子对撞机至关重要的高阶QCD校正的计算；例如在微扰展开中分别在四阶和三阶产生两个和三个射流。

项目成果

Non-linear non-renormalization theorems

• DOI: 10.1007/jhep08(2023)080
• 发表时间: 2023-03
• 期刊: Journal of High Energy Physics
• 影响因子: 5.4
• 作者: Weiguang Cao;F. Herzog;Tom Melia;Jasper Roosmale Nepveu

The double fermionic contribution to the four-loop quark-to-gluon splitting function

双费米子对四环夸克-胶子分裂函数的贡献

• DOI: 10.1016/j.physletb.2023.138351
• 发表时间: 2024
• 期刊: Physics Letters B
• 影响因子: 4.4
• 作者: Falcioni G

Four-loop splitting functions in QCD - The gluon-to-quark case

QCD 中的四环分裂函数 - 胶子到夸克的情况

• DOI: 10.1016/j.physletb.2023.138215
• 发表时间: 2023
• 期刊: Physics Letters B
• 影响因子: 4.4
• 作者: Falcioni G

The on-shell expansion: from Landau equations to the Newton polytope

壳上展开式：从朗道方程到牛顿多胞形

• DOI: 10.48550/arxiv.2211.14845
• 发表时间: 2022
• 期刊: arXiv e-prints
• 作者: Gardi Einan

Renormalization and non-renormalization of scalar EFTs at higher orders

• DOI: 10.1007/jhep09(2021)014
• 发表时间: 2021-05
• 期刊: Journal of High Energy Physics
• 影响因子: 5.4
• 作者: Weiguang Cao;F. Herzog;Tom Melia;Jasper Roosmale Nepveu