  The possibility of a dark sector weakly coupling to Standard Model (SM)
particles through new light mediators is explored at the Belle II experiment.
We present here results from three different searches, for a long-lived
(pseudo)scalar particle in rare $B$ decays; for a di-tau resonance in four-muon
final states, and the update on the search for a \zprime\ boson decaying
invisibly. We also look for lepton flavor violation by searching for
$\tau\rightarrow\ell \alpha$ decays, with $\alpha$ a new invisible boson, and
we report the first untagged reconstruction of $\tau$ pairs events searching
for the neutrinoless decays $\tau \to \ell \phi$. Finally, we present the
world's most precise measurement of the $\tau$ lepton mass. These studies are
performed on samples from the data collected by the Belle II detector during
2019-2021 data taking.
