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UBC Theses and Dissertations

Development of a Monte Carlo re-weighting method for data fitting and application to measurement of neutral B meson oscillations Asgeirsson, David J


In experimental particle physics, researchers must often construct a mathematical model of the experiment that can be used in fits to extract parameter values. With very large data sets, the statistical precision of measurements improves, and the required level of detail of the model increases. It can be extremely difficult or impossible to write a sufficiently precise analytical model for modern particle physics experiments. To avoid this problem, we have developed a new method for estimating parameter values from experimental data, using a Maximum Likelihood fit which compares the data distribution with a “Monte Carlo Template”, rather than an analytical model. In this technique, we keep a large number of simulated events in computer memory, and for each iteration of the fit, we use the stored true event and the current guess at the parameters to re-weight the event based on the probability functions of the underlying physical models. The re-weighted Monte-Carlo (MC) events are then used to recalculate the template histogram, and the process is repeated until convergence is achieved. We use simple probability functions for the underlying physical processes, and the complicated experimental resolution is modeled by a highly detailed MC simulation, instead of trying to capture all the details in an analytical form. We derive and explain in detail the “Monte-Carlo Re-Weighting” (MCRW) fit technique, and then apply it to the problem of measuring the neutral B meson mixing frequency. In this thesis, the method is applied to simulated data, to demonstrate the technique, and to indicate the results that could be expected when this analysis is performed on real data in the future.

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