Higgs production at NLO in the Standard Model Effective Field theory

The Effective Field Theory approach is a fruitful way of constraining new physics in a model independent way. As the Higgs sector is one of the most popular candidate for deviations from the Standard Model, it is particularly important that the constraints extracted from the experimental data on the Higgs boson be as meaningful as possible, which entails making accurate and precise theoretical predictions. In this proceeding, I discuss a two loop calculation performed to improve the existing Leading Order result for the Higgs gluon-fusion cross section in the Standard Model Effective Field Theory. We present the modern multi-loop calculation techniques employed to obtain this result and highlight the unusual divergence structure of the amplitude