An Unfolding Method for High Energy Physics Experiments

TL;DR

The paper tackles reconstructing the true spectrum from data affected by detector resolution and acceptance in high energy physics. It presents a modified RUN unfolding approach that fits Monte Carlo–generated distributions to the observed data in up to three dimensions using maximum likelihood, while accounting for finite MC statistics via Barlow's method with a new solution. A clustering step handles sparsely populated bins, and a data-driven regularization is applied after a diagonalization and rotation to keep bias minimal. The method integrates MC-based detector modeling, robust regularization, and adaptive bin handling to produce stable unfolded spectra suitable for experimental analyses.

Abstract

Finite detector resolution and limited acceptance require to apply unfolding methods in high energy physics experiments. Information on the detector resolution is usually given by a set of Monte Carlo events. Based on the experience with a widely used unfolding program (RUN) a modified method has been developed. The first step of the method is a maximum likelihood fit of the Monte Carlo distributions to the measured distribution in one, two or three dimensions; the finite statistic of the Monte Carlo events is taken into account by the use of Barlows method with a new method of solution. A clustering method is used before to combine bins in sparsely populated areas. In the second step a regularization is applied to the solution, which introduces only a small bias. The regularization parameter is determined from the data after a diagonalization and rotation procedure.