Wing Sheung Chan

110 Statistical interpretation and results e -veto BDT algorithm on true τ had - vis candidates at ± 1 σ , which is equivalent to 1.8% of the overall normalisations of the samples in the 3P SR. Jet → τ had - vis fakes As described in Section 5.5.2, the statistical uncertainties in the measured fake factors, as well as the statistical uncertainties in N fail r, data − N fail r, MC , real are considered. Luminosity The relative uncertainty in the measured integrated luminosity (1.7%) [129] is assigned to the overall normalisations of all the background MC samples except for the Z → τ τ sample, which is normalised by fitting a free parameter. Minor backgrounds For the minor backgrounds, theory uncertainties in the overall yields of the backgrounds are considered. These uncertainties are conservatively estimated and they include the overall uncertainties in the PDF, the strong coupling constant α s and the scale variations in the production of Higgs bosons, top quarks, dibosons and W ( → τν ) +jets. For the H → τ τ samples, a relative uncertainty of 4.1% in the total yield is assigned, which, aside from the Higgs production cross section, also accounts for the theory uncertainty in the H → τ τ branching fraction [118] . For the top-quark and diboson samples, relative uncertainties of 5% and 10% are assigned respectively [130, 131] . For the W ( → τν ) +jets samples, which have extremely minor contribution, a conservative 20% relative uncertainty is assigned. 6.2.2. Pruning and symmetrisation Some of the MC samples have a relatively small sample size in the SR or CRZ τ τ . For these samples, the estimated variations due to uncertainties might be dominated by statistical noise, which could introduce numerical instabilities in the fits. Moreover, uncertainties with little impact on the fit results can contribute to the complexity of the fits and lead to longer computation time. These uncertainties can be safely omitted without significantly affecting the final fit results. The removal of these uncertainties is also known as pruning. The following pruning and symmetrisation procedures are employed in order to stabilise and speed up the fit. They are performed on each uncertainty for each MC sample in each region. Samples with extremely low MC sample size Uncertainties of samples that have ex- tremely small MC sample size are completely removed from the fit. Having extremely