Deconvolving the detector in Fourier space

Abstract

We discuss algorithms for the analysis of hadronic final states, with application to single top t-channel production, heavy Higgs decaying as H → W+W- in the lepton plus jets mode, and others. In our examples, nature has arranged for the triple differential decay rates in angles we call θ1, θ2, ϕ to be a short finite series in orthogonal functions, √2πamk,lYmk (θ1, ϕ)Yml (θ2, 0) (summation implied), where the amk,l are complex constants. This observation can be exploited in two ways; first, a technique called orthogonal series density estimation may be employed to extract coefficients amk,l of the decay and physics parameters related to these coefficients; second, an angular analog of the convolution theorem may be employed to analytically deconvolve detector resolution effects from an observed signal.