Precise Perturbative Predictions for the Higgs Sector

在发现希格斯玻色子之后，大型强子对撞机（LHC）及其向高光度的升级（HL-LHC）进入了精密高能物理的新时代。这种精确度是做出新发现的关键，因为即使与当前模型有微小的偏差，也会为未知的粒子和相互作用提供重要的线索。然而，由于实验精度预计将超过目前的理论不确定性，该计划的成功将取决于我们克服提高理论预测准确性所面临的巨大挑战的能力。它需要计算高阶量子修正，这超出了现有方法的范围。这种复杂性和新的数学结构的出现迫使我们重新思考我们的策略。这个博士项目的第一部分将致力于开发新的方法，使多循环预测的有效计算。现代多回路计算的关键之一在于，最终需要计算的费曼积分的选择是自由的。这种自由度的一部分可以通过使用“分部积分恒等式（IBP）”来获得，该恒等式提供了一组出现在振幅中的积分之间的线性关系。最近在积分的分析计算方面取得的许多进展正是因为这种自由，通过选择一组特定的“规范”积分。事实上，用来表示振幅的积分的选择在回路计算中起着更深的作用;它允许振幅的一些物理性质变得明显。例如，振幅中的伪奇异性可以通过明智地选择积分来避免。具体地说，作为这个项目的一部分，将研究在主积分的有限基中表达振幅的新方法。在这一领域有许多令人兴奋的想法还有待充分探讨：强制积分在阈值附近具有正确的行为，利用振幅的IR/UV奇异性的知识，以及使用振幅的高能量和小质量限制的知识。作为这个项目的一个重要工具，一个更正式的，分析，理解这一主题可以通过使用所谓的“相交理论”。博士项目的第二部分将应用新的方法来计算高阶微扰QCD/EW修正的相关过程的希格斯部门在LHC/HL-LHC和预期的未来对撞机。在这种情况下，2-loop EW校正几个环路引起的希格斯通道是目前未知的，将是主要的候选人使用开发的技术进行研究。例如，pp -> HH过程对希格斯玻色子的自耦合直接敏感，并使实验能够获得希格斯势的结构。pp -> H +喷流过程是在LHC上探索顶夸克阈值以上希格斯扇区的关键途径之一。目前，对这些过程的最佳预测是使用混合方法产生的：在重顶夸克极限下的N3 LO或NNLO QCD修正由完整的NLO QCD预测重新加权。天真地，我们可以预期，目前未知的NLO EW效应在相空间的某些区域可能与这些NNLO QCD校正的大小相似，并且它们将在高能处增长，这是寻找新物理的最有趣的区域。事实上，NLO EW对更简单的二比一过程pp -> H的修正已经知道了一段时间，作为希格斯玻色子质量的函数，它们使总截面移动了5%。计算目前未知的2-loop EW修正的过程中相关的研究希格斯部门是这个博士项目的目标。

After the discovery of the Higgs boson, the Large Hadron Collider (LHC) and its upgrade to high luminosity (HL-LHC) have entered a new era of precision high-energy physics. This precision is the key to making new discoveries, as even slight deviations from the current model will provide important hints to as yet unknown particles and interactions. However, with experimental precision expected to outstrip current theoretical uncertainties, the success of this program will rely on our ability to overcome the immense challenges involved in improving the accuracy of our theoretical predictions. It requires the calculation of higher-order quantum corrections which are beyond the scope of current methods. This complexity and the appearance of new mathematical structures force us to rethink our strategy.The first part of this PhD project will be dedicated to developing new methods to enable the efficient calculation of multi-loop predictions. One of the keys to modern multi-loop calculations lies in the fact that there is a freedom in the choice of Feynman integrals that ultimately need to be calculated. Part of this freedom can be accessed through the use of "integration-by-parts identities (IBPs)" which provide a set of linear relations between the integrals appearing in the amplitude. Much of the recent progress in the analytic evaluation of integrals was made possible exactly because of this freedom, through the choice of a particular set of "canonical" integrals. In fact, the choice of integrals used to express the amplitude plays a much deeper role in loop calculations; it allows some of the physical properties of the amplitude to be made manifest. For example, spurious singularities in the amplitude can be avoided through a judicious choice of integrals. Concretely, as part of this project, new methods for expressing amplitudes in a finite basis of master integrals free of spurious singularities will be investigated. There are many exciting ideas in this area yet to be fully explored: enforcing that integrals have the correct behaviour near to threshold, exploiting knowledge of the IR/UV singularities of the amplitude, and using knowledge of the high-energy and small mass limits of the amplitude. As an important tool for this project, a more formal, analytic, understanding of this topic may be obtained through the use of so-called "intersection theory".The second part of the PhD project will apply the new methods to compute higher-order perturbative QCD/EW corrections to processes of relevance for the Higgs Sector at the LHC/HL-LHC and anticipated future colliders. In this context, the 2-loop EW corrections to several loop-induced Higgs channels are currently unknown and would be prime candidates for study using the developed techniques. For example, the pp -> HH process is directly sensitive to the Higgs boson self-couplings and enables experimental access to the structure of the Higgs potential. The pp -> H + jet process is one of the key avenues for exploring the Higgs sector at the LHC above the top quark threshold. Currently, the best predictions for these processes are produced using a hybrid approach: the N3LO or NNLO QCD corrections in the heavy top-quark limit are re-weighted by the full NLO QCD prediction. Naively, we may expect that the currently unknown NLO EW effects could be of a similar size to these NNLO QCD corrections in some regions of phase-space and that they will grow at high-energy, the most interesting region in which to search for new physics. In fact, NLO EW corrections to the simpler two-to-one process pp -> H have been known for some time as a function of the Higgs boson mass, they shift the total cross-section by 5%. The computation of the currently unknown 2-loop EW corrections to a process relevant for studying the Higgs sector is a goal of this PhD project.