Exploring anomalous couplings in Higgs boson pair production through shape analysis

We classify shapes of Higgs boson pair invariant mass distributions $m_{hh}$, calculated at NLO with full top quark mass dependence, and visualise how distinct classes of shapes relate to the underlying coupling parameter space. Our study is based on a five-dimensional parameter space relevant for Higgs boson pair production in a non-linear Effective Field Theory framework. We use two approaches: an analysis based on predefined shape types and a classification into shape clusters based on unsupervised learning. We find that our method based on unsupervised learning is able to capture shape features very well and therefore allows a more detailed study of the impact of anomalous couplings on the $m_{hh}$ shape compared to more conventional approaches to a shape analysis.