Flavour Changing Neutral Current decays at LHCb

Abstract: Flavour Changing Neutral Current (FCNC) decays are forbidden at lowest perturbative order in the Standard Model (SM) and only allowed via quantum loops. These transitions are therefore heavily suppressed in the SM, and New Physics (NP) can give significant contributions through virtual corrections. Of particular interest are semileptonic $b\to s(d)\ell<sup>+\ell<sup>-$ and radiative $b\to s(d)γ$ decays that allow to not only to search for the presence of NP, but also probe its potential operator structure through a multitude of observables. These observables include measurements of branching fractions, angular observables, CP-asymmetries and tests of lepton flavour universality. Long-standing tensions of data with SM predictions have been observed in $b\to sμ<sup>+μ<sup>-$ decays, consistently in measurements of branching fractions and angular analyses. However, the significance of these tensions depends on assumptions on hadronic uncertainties in the SM prediction. These proceedings summarise the most recent results on FCNC decays from the LHCb experiment, including the legacy measurement of the key decay $B^0\to K<sup>{*0}μ<sup>+μ<sup>-$, using $8.4\mathrm{fb}<sup>{-1}$ of data from the LHC Run 1 and 2.