Next-to-Leading Order QCD Corrections to Higgs Boson Production and Mixed QCD-Electroweak Corrections to Z Boson Production at High Transverse Momentum

In this thesis we study two processes: the Higgs boson production when the Higgs transverse momentum larger than the top-quark mass $p_{H,T}\gg m_t$ and the Z boson production at high transverse momentum. The key point of our study is the evaluation of master integrals. Both processes share a similar signature at the high transverse momentum: a hierarchy of scales. This signature is exploited to construct asymptotic expansions of master integrals which allows us to simplify their evaluation. Master integrals are then evaluated using differential equations. The analytical results are expressed in terms of Goncharov polylogarithms. In the case of the Higgs boson production, the evaluation of relevant master integrals allows us to compute two-loop amplitudes for partonic processes $gg\to Hg,\, q\bar{q}\to Hg$ and $qg\to Hg$. These two-loop amplitudes are the long-missing part of next-to-leading order QCD corrections to the Higgs+jet production at high-$p_{H,T}$. The evaluation of next-to-leading order QCD corrections increases the exiting leading-order results by almost a factor of two. This result removes one of the largest theoretical uncertainties in the description of the Higgs+jet production at large-$p_{H,T}$.