Abstract: Lepton Flavour Violation (LFV) being forbidden in the Standard Model, LFV searches represent a powerful probe for New Physics. Studying $B^0 \rightarrow K^{*0} \tau \ell$ decays, where $\ell$ is an electron or muon, is particularly interesting: it allows to explore both $b \rightarrow s\ell\ell'$ transitions and the third generation coupling with $\tau$ leptons which could be more sensitive to New Physics.
The Belle II experiment is located at the SuperKEKB $e^+e^-$ collider at KEK, and collected a total of 365 fb$^{-1}$ of data at the $\Upsilon(4S)$ resonance ($10.58~\text{GeV}$) during its first data taking period, from 2019 to 2022. Designed to produce $B\bar{B}$ pairs in a clean environment and almost hermetic detector, the Belle II experiment provides a well-suited environment for the study of $B^0 \rightarrow K^{*0} \tau \ell$ decays, where the partner $B$ meson from the $B\bar{B}$ pair production is reconstructed hadronically.
This analysis uses a cut-based selection coupled to machine learning techniques to reject the background. An upper limit on the $B^0 \rightarrow K^{*0} \tau \ell$ branching fraction is extracted from a fit to the recoil mass of the $\tau$ lepton.