Test of lepton flavour universality using hadronic tau decays with the LHCb detector

The goal of this internship was to realize a preliminary study on the measurement of the $R$($D$$^{∗}$) parameter, defined as the ratio between the two branching fractions${\cal{R}}(D^{*-})\equiv {\cal{B}}(B^0 \to D^{*-} \tau^+ \nu_{\tau})/{\cal{B}}(B^0 \to D^{*-} \mu^+\nu_{\mu})$, using the τ$^{+}$ → π$^{+}$ π$^{−}$ π$^{+}$$\nu$$_{τ}$ hadronic decays recorded by the LHCb detector. The world average on the measurements done so far shows a discrepancy of 3.4 standard deviations with respect to the Standard Model prediction. This points towards Lepton Flavor Universality Violation and needs to be investigated further. So far, the Run 2 (2015-2018) data had never been exploited for the measurement of $R$($D$$^{∗}$) and a first look was made during this internship. Between Run 1 (2011-2012) and Run 2, the LHC center-of- mass energy increased and the LHCb trigger was improved. Lower statistical error is expected on measurements performed on Run 2 data. The gain in performance due to the improved trigger is evaluated to be 15.3%. Finally, the gain factor brought by Run 2 enhancements to event yields is evaluated to be 5.0 ± 0.2, so that the statistical error on future measurements of the $R$($D$$^{∗}$) parameter with the LHCb detector would decrease from 6.7% to 3.0%.