An Unfolding Method for High Energy Physics Experiments

By V. Blobel. 2002

136 citations recorded by the source corpus.

Finite detector resolution and limited acceptance require one 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 statistics of the Monte Carlo events is taken into account by the use of Barlow’s method with a new method of solution. A clustering method is used before combining 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. 1 THE UNFOLDING PROBLEM A standard task in high energy physics experiments is the measurement of a distribution of some kinematical quantity . With an ideal detector one could measure the quantity in every event and could obtain by a simple histogram of the quantity . With real detectors the determination of is complicated by three effects: Limited acceptance: The probability to observe a given event, the detector acceptance, is less than 1. The acceptance depends on the kinematical variable . Transformation: Instead of the quantity a different, but related quantity is measured. The transformation from to can be caused by the non-linear response of a detector component. Finite resolution: The measured quantity is smeared out due to the finite resolution (or limited measurement accuracy) of the detector. Thus there is only a statistical relation between the true kinematical variable and the measured quantity . The really difficult effect in the data correction for experimental effects, or data transformation from to is the finite resolution, causing a smearing of the measured quantities. Mathematically the relation between the distribution of the true variable , to be determined in an experiment, and the measured distribution of the measured quantity is given by the integral equation, d (1) called a Fredholm integral equation of the first kind. In practice often a known (measured or simulated) background contribution has to be added to the right-hand side of equation (1); this contribution is ignored in this paper. The resolution function represents the effect of the detector. For a given value the function describes the response of the detector in the variable for that fixed value . The problem in determining the distribution from measured distributions is called unfolding; it is called an inverse problem. Unfolding of course requires the knowledge of the resolution function , i.e. all the effects of limited acceptance, transformation and finite resolution.

Subfields: Artificial Intelligence, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/29030bc637190ce07b19a7c624f876b5b771ac57

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Nuclear and High Energy Physics

Citations in the corpus

Measurement of the differential cross section for top quark pair production in pp collisions at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin} (2015, methodology): “The unfolded results are found to be consistent with those obtained using other regularization techniques [46].”