Relative Morsification Theory

In this paper we develope a Morsification Theory for holomorphic functions defining a singularity of finite codimension with respect to an ideal, which recovers most previously known Morsification results for non-isolated singulatities and generalize them to a much wider context. We also show that deforming functions of finite codimension with respect to an ideal within the same ideal respects the Milnor fibration. Furthermore we present some applications of the theory: we introduce new numerical invariants for non-isolated singularities, which explain various aspects of the deformation of functions within an ideal; we define generalizations of the bifurcation variety in the versal unfolding of isolated singularities; applications of the theory to the topological study of the Milnor fibration of non-isolated singularities are presented. Using intersection theory in a generalized jet-space we show how to interprete the newly defined invariants as certain intersection multiplicities; finally, we characterize which invariants can be interpreted as intersection multiplicities in the above mentioned generalized jet space.Comment: 56 pages, some typos correcte

Next-to-Next-to-Leading Order QCD Corrections to Higgs Boson Pair Production

We present the Higgs boson pair production cross section at next-to-next-to-leading order in QCD within the large top-mass approximation. Numerical results for the LHC are provided, finding an increase of O(20%) with respect to the previous order prediction and a substantial reduction in the scale dependence. We normalize our results using the full top- and bottom-mass dependence at leading order.Comment: Proceedings of 'Loops & Legs 2014', Weimar (Germany), April/May 201

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Higgs Boson Pair Production at Next-to-Next-to-Leading Order in QCD

We compute the next-to-next-to-leading order QCD corrections for Standard Model Higgs boson pair production inclusive cross section at hadron colliders within the large top-mass approximation. We provide numerical results for the LHC, finding that the corrections are large, resulting in an increase of ${\cal O}(20$ with respect to the next-to-leading order result at c.m. energy $\sqrt{s_H}=14\,\text{TeV}$. We observe a substantial reduction in the scale dependence, with overlap between the current and previous order prediction. All our results are normalized using the full top- and bottom-mass dependence at leading order. We also provide analytical expressions for the K factors as a function of $s_H$