Wing Sheung Chan

Statistical interpretation and results 111 small MC sample size is defined as having an overall relative statistical error larger than 10% in the concerned region. In this analysis, samples that have extremely small MC sample size include W ( → τν ) +jets in the both the 1P and 3P SR and CRZ τ τ , and Z → `` in the 3P regions. Removal of normalisation effects The effect of an uncertainty on the overall normalisa- tion of a sample is kept only when its impact at ± 1 σ is larger than 0.1% of the total nominal yield. Removal of shape effects In order to test if the effect of an uncertainty on the shape of the expected distribution is significant compared to the MC statistical uncertainties, a χ 2 test is performed between the normalised nominal distribution and the varied distribution at ± 1 σ . Only if the corresponding p -value from the χ 2 test is smaller than 0. 9 † . The effect of an uncertainty on the distribution shapes is always kept for uncertainties in efficiency scale factors. Symmetrisation Sometimes, due to statistical fluctuation, variations due to uncertainties could be one-sided in certain bins, i.e. the +1 σ and − 1 σ variations of the expected yield are both larger than or both smaller than the nominal expected yield. These variations are symmetrised by inverting the direction of the smaller variation. 6.2.3. Impact on the best-fit LFV branching fraction A summary of the postfit uncertainties and their impact on the best-fit LFV branching fraction is given in Table 6.1. It shows that the primary source of uncertainty in the analysis is statistical. This is mainly due to the fact that the fakes modelling and the normalisation of the Z → τ τ background are both determined using data. This heavily data-driven modelling approach is what allows the analysis to make full use of the data, without being heavily limited by uncertainties in theoretical calculations and simulations. The remaining dominant uncertainties are those in the TES and in the e → τ had - vis misidentification modelling. 6.3. Results The observed and the best-fit expected distributions of the combined NN output in the SR and the collinear mass in CRZ τ τ are shown in Figures 6.1 and 6.2 for the eτ and µτ channels respectively. The corresponding best-fit POIs and NFs are listed in Table 6.2. Almost no signal is fitted in the eτ channel, while a small positive signal is fitted in the µτ channel. The precision of the determined yields of Z → τ τ events and fakes ranges from 2% to 4%. † Note that a smaller p -value in a χ 2 test represents more confidence for rejecting the hypothesis of identity.