From Ising Model to Collider Graphs

This note records how an open question about symmetry—why do symmetric physical lawsproduce asymmetric outcomes?—led me, step by step, to a narrow and testable questionin collider physics: how does the way we build a graph from a collision event affect what a graphneural network (GNN) can learn from it? I first use the Ising model and a toy Higgs potential tobuild intuition for symmetry and symmetry breaking. I then show, with working code, how asingle collision event becomes a graph: reconstructed leptons and jets become nodes, and theirangular separations become edges. On an illustrative t¯tH, H → ZZ∗ → 4ℓ event built fromreal kinematics, my four-lepton candidate finder recovers the input Higgs mass of 125.00 GeV,and I verify numerically that the graph’s edge features are unchanged by reordering theobjects or rotating the event around the beam. Finally, I describe the planned study on publicCMS 2016 simulation [1, 2], the safeguards needed to make it fair, and its current status. Nophysics result is claimed here: this is a record of understanding and method, written so thateach step can be checked.