Wing Sheung Chan

Statistical interpretation and results 115 Table 6.3.: The expected (median) and observed upper limits on the signal branching fraction at 95% CL, under different assumptions for the τ -polarisation state. The difference between the observed and expected limits are due to the non-zero best-fit signal branching fractions. Experiment, τ -polarisation state assumption Observed (expected) upper limit on B ( Z → `τ ) [ 10 − 6 ] eτ µτ ATLAS Run 2, unpolarised 8.1 (8.1) 9.9 (6.3) ATLAS Run 2, left-handed 8.2 (8.6) 9.5 (6.7) ATLAS Run 2, right-handed 7.8 (7.6) 10 (5.8) ATLAS Run 1, unpolarised [132] 17 (26) ATLAS Run 1 and Run 2, unpolarised (see Sec- tion 6.4) 9.5 (6.1) OPAL, unpolarised [58] 9.8 17 DELPHI, unpolarised [60] 22 12 The best-fit NFs and NPs for systematic uncertainties, ranked in their estimated impact on the best-fit POI, are summarised in Figures 6.3 and 6.4 for the eτ and µτ channels respectively. Only the highest ranked 40 parameters are shown. As expected, uncertainties related to the TES and fakes modelling have the highest impact on the POI. Additionally, in the eτ channel, the e → τ had - vis fakes correction scale factors are also a dominant source of uncertainty. Some of the TES NPs appear to be pulled by the fit away from their prefit values, especially in the µτ channel. This is reasonable as the prefit estimated values and uncertainties for these NPs are not entirely applicable to this analysis, as already discussed in Section 6.2. The p -values (significance) for the null hypotheses in the eτ and µτ channels are 0.99 ( − 2 . 17 σ ) and 0.18 ( 0 . 90 σ ) respectively. Since no significant excess in data is observed, exclusion upper limits on the LFV signal branching fractions are set. For all the three considered scenarios with different assumed τ -polarisation states and Z`τ interaction vertices, the corresponding upper limits at 95% confidence level (CL) are shown in Table 6.3. For comparison, existing upper limits from the LEP experiments and from previous measurement by ATLAS are also shown in the same table. The observed upper limits on B ( Z → eτ ) and B ( Z → µτ ) at 95% CL under the assumption of parity-conserving Z`τ vertices are 8 . 1 × 10 − 6 and 9 . 9 × 10 − 6 respectively. As can be seen from the table, the observed upper limits set by this analysis superseded those set by the LEP experiments, which are otherwise the most stringent limits established, for the first time in over two decades. Since it is shown that the sensitivity of this analysis is