Wing Sheung Chan

Chapter 6. Statistical interpretation and results Nothing in the world causes so much misery as uncertainty. — Martin Luther To interpret the observed data, binned maximum-likelihood fits are used to compare observations with predictions and to extract evidence of possible signal events. The significance of any possible excess in data is assessed, and the background-only (null) and background-plus-signal (alternative) hypotheses are tested. In case no significant excess in data is observed, exclusion upper limits on the LFV branching fractions are set by inverting the hypothesis tests. This chapter details the methods and results of the statistical interpretation for the analysis. 6.1. Maximum-likelihood fit For each of the eτ and µτ channels, a binned maximum-likelihood fit to data is used to compare the expected distributions of the combined NN output in the SR and the collinear mass in CRZ τ τ with the observed distributions, and to extract evidence of possible signal events. The high-NN-output region of the SR is sensitive to the signal, which allows the fit to determine the potential signal yield precisely. Meanwhile, the low-NN-output region of the SR is enriched in background events and can be used by the fit to constrain the background predictions. Furthermore, the m coll ( `, τ ) distribution in CRZ τ τ is utilised by the fit to improve the precision of the determined Z → τ τ yields, as well as the constraints on the TES related uncertainties, which are both factors that significantly impact the signal sensitivity. Due to the differences in acceptances, efficiencies and background compositions, 1P and 3P regions are considered separately in the fit. The probability of compatibility between the data and the background-only or background- plus-signal hypothesis is assessed using the modified frequentist CL s method [123] , and exclusion upper limits on B ( Z → `τ ) are set by the inversion of these hypothesis tests in case of no significant discovery. 105