Precision calculations in effective theories for Higgs production

The Standard Model (SM) models the behavior of the known elementary particles and describes correctly most known physical phenomena that happen between human and subatomic scales. Despite the success of the SM, we know that it cannot be the ultimate theory of nature because it fails to explain a number of observations, such as the existence of dark matter. As a result, much activity has been devoted to finding deviations from the SM, which requires precise theoretical predictions that can be compared to experiments. My thesis is part of the effort to improve our predictions for Higgs boson production so that we can probe the SM at colliders such as the LHC. This manuscript describes two projects. The first provides a tool for the improvement of the prediction for the associated production of a Higgs boson with bottom quarks: the first power-suppressed correction to the bottom-quark Yukawa in the Higgs effective field theory (HEFT). To this end, we performed the matching of a form factor for the Higgs boson decay to bottom quarks between the HEFT and the SM. The second project consisted in the evaluation of the next-to-leading order corrections to the production of a Higgs boson in gluon fusion in the SM effective field theory. We describe the analytic calculation required to obtain this result and provide phenomenological result showing the impact of dimension six operators on Higgs boson production at the inclusive and differential level.(SC - Sciences) -- UCL, 201