Recursive Jigsaw Reconstruction: HEP event analysis in the presence of kinematic and combinatoric ambiguities

We introduce $Recursive~Jigsaw~Reconstruction$, a technique for analyzing reconstructed particle interactions in the presence of kinematic and combinatoric unknowns associated with unmeasured and indistinguishable particles, respectively. By factorizing missing information according to decays and rest frames of intermediate particles, an interchangeable and configurable set of $Jigsaw~Rules$, algorithms for resolving these unknowns, are applied to approximately reconstruct decays with arbitrarily many particles, in their entirety. That the Recursive Jigsaw Reconstruction approach can be used to analyze $any$ event topology of interest, with any number of ambiguities, is demonstrated through a twelve different simulated LHC physics examples. These include the production and decay of $W$, $Z$, Higgs bosons, and supersymmetric particles including gluinos, stop quarks, charginos, and neutralinos.