BBJAmps · Massive 2 to 3 two-loop amplitudes in asymptotic limits for collider phenomenology

The data taken at the Large Hadron Collider (LHC) at CERN and its future High-Luminosity upgrade enables the study of the fundamental interactions of matter at unprecedented precision and energy. After the discovery of the Higgs boson one of the major goals of the LHC is the precise measurement of its properties. In order to achieve the needed theoretical precision, two-loop corrections to many scattering amplitudes have to be computed.A crucial process to precisely determine the coupling of the Higgs boson to the bottom quark is the production of a Higgs, a Z-boson, and a jet. This process receives large contributions and accompanying uncertainties from the sub-process of gluon fusion, which only starts contributing at the one-loop level but is enhanced by the large gluon luminosity at hadron colliders. To improve the theoretical description of this sub-process and enable the most precisedetermination of the Higgs-bottom coupling, the two-loop five-point amplitudes of this sub-process will be computed in this project. The results of this project can also be applied to double Higgs production, which the crucial experimental signature to determine the Higgs self-interaction at hadron colliders in the future.The computation of five-point amplitudes with massive internal and external particles is a tremendously difficult task, due to the algebraic complexity of the amplitudes and the appearance of new classes of special functions. To tackle and circumvent some of the difficulties I will explore the systematic approximation of these complicated amplitudes in various kinematic limits, like small Mandelstam variables or the high-energy limit. This methodology has already proven successful for two-loop four-point amplitudes previously. The results of this project will, therefore, significantly enhance our ability to obtain precise theory predictions for high-multiplicity processes and simplify their calculation and numerical evaluation.