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Rare FCNC top, beauty and charm decays

Rare flavour changing neutral current (FCNC) decays of top, beauty and charm quarks can provide a powerful probe for as yet unobserved particles. Recent results on FCNC $b \to s$, $c \to u$ and $t$ transitions from the LHC experiments are reviewed. Particular attention is paid to the angular distribution of the $B^{0} \to K^{*0} μ^{+} μ^{-}$ decay, where a measurement performed by LHCb shows a local discrepancy of 3.7 standard deviations with respect to the SM prediction. Using the decay $B^{+} \to K^{+}π^{-}π^{+}γ$, LHCb have also been able to demonstrate the polarisation of photons produced in $b \to sγ$ transitions. More work is needed both experimentally and theoretically to understand if the Standard Model description of these rare FCNC processes is correct.