New Physics Searches with $b\to s\ell^+\ell^-$ Transitions and Rare Decays at LHCb

Several tensions between the experimental measurements and their Standard Model predictions have been observed in rare $B$ meson decays mediated by $b\to s\ell^+\ell^-$ transitions. To understand the nature of these discrepancies, the LHCb experiment is extending its previously reported studies with additional observables and decay modes. These proceedings summarise the latest results on the topic. They report on a measurement of the interference between the long- and short-distance contributions in $B^+\to K^+\mu^+\mu^-$ decays, on the searches for the $B\to \mu^+\mu^-\mu^+\mu^-$ and $B\to\tau^+\tau^-$ decays, and present an update of the $B\to \mu^+\mu^-$ analysis, which includes the first measurement of the $B_s^0\to \mu^+\mu^-$ effective lifetime.