Precise Perturbative Predictions for the Higgs Sector

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.