Precision Calculations for Higgs Boson Physics at the LHC - Four-Loop Corrections to Gluon-Fusion Processes and Higgs Boson Pair-Production at NNLO

The search for the pair-production of the Higgs boson and the precise study of its
properties are among the corner stones of the physics programme of the Large Hadron
Collider and its High-Luminosity upgrade.
This thesis focuses on the evaluation of higher-order corrections to Higgs boson pair
production: the effective two-Higgs boson–gluon coupling at four loops and next-to-next-
to-leading order corrections to the total inclusive cross-section including finite top-quark
mass effects.
In addition, finite top-quark mass effects in the Higgs boson–gluon vertex are studied
at the four-loop order and four-loop corrections to the Higgs boson decay into photons
are obtained.