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As I understand it, they didn't see the Higgs particle. The Higgs particle is so short-lived that it cannot directly be detected by any currently available technique or equipment. The only way in which the existence of the Higgs particle can be inferred is by the identification of the smaller particles into which it decays. Around half a century of theoretical work has enabled scientists to identify, theoretically, these decay products and find ways of distinguishing them from the vast numbers of particles produced in the billions of collisions generated in the LHC. It is these decay products that were detected, and identified by the international group of scientists gathered at CERN.
how did know they saw the Higgs Boson?