Precision calculations in effective theories for Higgs production

After a general introduction, this manuscript presents two preliminary chapters, describing first the physics context and the mathematical techniques used in this thesis.We then present the work performed in this thesis. We start with extraction of the power-suppressed of the Yukawa coupling of the bottom quark in the Higgs Effective Field Theory (HEFT) by a two-loop matching calculation between the Standard Model and the HEFT. This correction was the missing piece to improve the prediction of the production cross section of a Higgs boson in association to a pair of bottom quarks.The two next chapters present different aspects of the NLO corrections to Higgs boson production through gluon fusion in the standard model effective field theory. We first present the evaluation of the virtual corrections to this process and use the known one-loop ultraviolet and infrared divergence structure to extract a two-loop counterterm that allowed us to renormalize the amplitude, which we then analytically continued to the physical regions.We then combine this result with the automatic calculation of the real emission corrections in the program Madgraph5_aMC@NLO. The results are presented for the total cross section and differential distributions and comment on the effect of radiative corrections on these predictions

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