Fourier Transforms as a tool for Analysis of Hadron-Hadron collisions

Abstract

Hadronic final states in hadron-hadron collisions are often studied by clustering final state hadrons into jets, each jet approximately corresponding to a hard parton. The typical jet size in a high energy hadron collision is between 0.4 and 1.0 in eta-phi. On the other hand, there may be structures of interest in an event that are of a different scale to the jet size. For example, to a first approximation the underlying event is a uniform emission of radiation spanning the entire detector, colour connection effects between hard partons may fill the region between a jet and the proton remnant and hadronisation effects may extend beyond the jets. We consider the possibility of performing a Fourier decomposition on individual events in order to produce a power spectrum of the transverse energy radiated at different angular scales. We attempt to identify correlations in the emission of radiation over distances ranging from the full detector size to approximately 0.2 in eta-phi. As a demonstration of this technique we apply it to a comparison of di-jet events produced with and without a colour connection between the jets.