What Do Event Generators Compute? Flux Functionals from Detector Operators

Abstract

Every physical prediction of an event generator is a statement about the hadronic fluxes that can be recorded by particle detectors. By contrast, the formal backbone of modern event-generator precision is provided by the unobservable partonic final states of the parton shower, with hadronisation included as a model. We construct the probability distribution of the hadronic fluxes non-perturbatively, directly from detector operators acting on asymptotic hadronic states, and encode it in an event generator source functional. This distribution contains every measurement a detector can make, and is therefore what a generator must compute with precision, including the effects of hadronisation. Restricting the functional to the energy flow yields the parton shower source functional, which is infrared and collinear safe and contains every calorimetric observable, making it a natural object against which to assess parton-shower accuracy. We compute its logarithmic structure at one loop in $e^+e^-$ annihilation, finding it directly sensitive to kinematic recoil and hence to the recoil scheme of a parton shower. The parton shower functional depends on a continuum of low scales, one for each resolved direction, and in a toy model its logarithms cannot be entirely resummed within a factorisation whose evolution derives only from the high-scale physics. Our operator-based formulation opens the door to the study of event-generator-like systems in theories beyond QCD, including conformal theories such as $N=4$ super-Yang-Mills theory, and thereby offers a new route to non-perturbative insight into event generation.