Intrinsic geometry of collider events and nearest neighbour based weighted filtration

Abstract

Collider observations have mainly been studied on an event-by-event basis, leveraging several kinematic techniques. However, the intrinsic topological imprints of the ensemble of new physics events can be strikingly different from the SM background ensemble. Traditional topological data analysis (TDA) is known for its stability against small perturbations. However, a plethora of rich information encoded in the clustering of ensembles is often lost due to the unweighted filtration of simplicial complexes. Taking a singlet extended model as an example, this work illustrates the rich global properties associated with the so-called distance-to-measure (DTM) filtration on Alpha complexes using weights determined from k-nearest neighbours.Comment: 1 table, 7 figure