  Topological invariants have played a fundamental role in the advancement of
theoretical high energy physics. Physicists have used several kinematic
techniques to distinguish new physics predictions from the Standard Model (SM)
of particle physics at Large Hadron Collider (LHC). However, the study of
global topological invariants of the collider signals has not yet attracted
much attention. In this article, we present a novel approach to study collider
signals using persistent homology. The global topological properties of the
ensemble of events as expressed by measures like persistent entropy, Betti
area, etc. are worth considering in addition to the traditional approach of
using kinematic variables event by event. In this exploratory study, we first
explore the characteristic topological signature of a few SM electroweak
resonant productions. Next, we use the framework to distinguish global
properties of the invisible Higgs decay processes in the SM and a real singlet
extension of the SM featuring stable singlet scalar dark matter.
