Collider Field Study

We present a novel theoretical framework that unifies fractal energy-flow geometry with

topological field classification methods in high-energy proton-proton (pp) collisions at the

Large Hadron Collider (LHC). The central construction introduces a Riemannian phase-space

manifold parameterized by per-particle kinematic observables, on which a heat-equationtype geometric flow governs the evolution of jet energy distributions. We define a family of

fractal observables — including the box-counting fractal dimension Df and the multifractal

generalized dimensions Dq — that characterize the self-similar structure of energy deposits

on the (η, φ) cylinder, and propose these as robust quark/gluon jet discriminants with

complementarity to classical substructure variables such as N-subjettiness and D2.

Topological anomaly classification is achieved through persistent homology applied to

particle-level event point clouds, yielding a model-agnostic anomaly score based on the

Wasserstein-2 distance between persistence diagrams. We demonstrate expected area-underthe-ROC-curve (AUC) values of 0.74 for quark/gluon separation and 0.81–0.91 for Beyond

Standard Model (BSM) signal discrimination against QCD multi-jet backgrounds. A fully

reproducible, open-source analysis pipeline — spanning Monte Carlo generation, detector

simulation, jet reconstruction, and statistical inference — is described in detail. All code and benchmark datasets are released under FAIR data principles, with integration into the

REANA platform at CERN. The framework provides a new avenue for BSM searches in Run 3

and the High-Luminosity LHC era.