Precise Perturbative Predictions for the Higgs Sector

在发现希格斯玻色子后，大型强子对撞机(LHC)及其向高光度(HL-LHC)的升级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稍有偏离，也会为未知的粒子和相互作用提供重要的线索。然而，随着实验精度有望超过目前理论上的不确定性，这个项目的成功将取决于我们克服提高理论预测准确性所涉及的巨大挑战的能力。它需要计算高阶量子修正，这超出了当前方法的范围。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战略。这个博士项目的第一部分将致力于开发新的方法，以实现多循环预测的高效计算。现代多循环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，该恒等式提供了出现在振幅中的积分之间的一组线性关系。最近在积分分析评估方面的许多进展正是由于这种自由，通过选择一组特定的“正则”积分而成为可能的。事实上，用于表示幅度的积分的选择在循环计算中起着更深层次的作用；它允许显示幅度的一些物理属性。例如，通过明智地选择积分，可以避免振幅中的虚假奇点。具体地说，作为这个项目的一部分，我们将研究在没有伪奇点的主积分的有限基上表示振幅的新方法。在这一领域有许多激动人心的想法还有待充分探索：强制积分在阈值附近具有正确的行为，利用幅度的IR/UV奇异性的知识，以及利用幅度的高能和小质量限制的知识。作为这个项目的一个重要工具，可以通过使用所谓的“交集理论”来获得对这个主题的更正式、更解析的理解。PHD项目的第二部分将应用新的方法来计算与LHC/HL-LHC和预期的未来对撞机上的Higgs部门相关的过程的高阶微扰QCD/EW修正。在这种情况下，对几个环诱导的希格斯信道的双环EW校正目前是未知的，并且将是使用所开发的技术进行研究的主要候选者。例如，pp-&gt；hh过程对希格斯玻色子自耦合直接敏感，并使我们能够通过实验获得希格斯势的结构。Pp&gt；H+喷注过程是探索大型强子对撞机上高于最高夸克阈值的希格斯部门的主要途径之一。目前，对这些过程的最佳预测是使用一种混合方法：重顶夸克极限中的N3LO或NNLO QCD修正由完整的NLO QCD预测重新加权。我们可能会天真地认为，目前未知的NLO EW效应可能与相空间某些区域中的NNLO QCD校正的大小相似，并且它们将在高能区域生长，这是寻找新物理的最感兴趣的区域。事实上，对更简单的二对一过程pp&gt；H的NLO EW修正作为希格斯玻色子质量的函数已经被知道了一段时间，它们使总截面移动了5%。对与研究希格斯扇区相关的过程的目前未知的双环EW修正的计算是本博士项目的目标。

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.