Search for an invisible boson in tau decays with early Belle II data and development of new analysis methods for tau physics

This thesis searches for "tau to lepton + invisible". We search with 62.8 fb${}^{-1}$ of Belle II data and find no evidence for this decay. We determine an upper limit in the range of 1‰ to 1% for the ratio of branching ratios. This thesis contributed to Belle II performance studies. We develop and test new tau-rest frame estimation methods and find that one (the GKK method) shows perspectives to substantially enhance the statical precision of the tau mass measurement.