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The system of two transiting Neptune-sized planets around the bright, youngM-dwarf AU Mic provides a unique opportunity to test models of planetformation, early evolution, and star-planet interaction. However, the intensemagnetic activity of the host star makes measuring the masses of the planetsvia the radial velocity (RV) method very challenging. We report on a 1-year,intensive monitoring campaign of the system using 91 observations with theHARPS spectrograph, allowing for detailed modelling of the $\sim 600\,\rm{m\,s^{-1}}$ peak-to-peak activity-induced RV variations. We used amultidimensional Gaussian Process framework to model these and the planetarysignals simultaneously. We detect the latter with semi-amplitudes of $\rm{K_b}= 5.8 \pm 2.5\, \rm{m\,s^{-1}}$ and $\rm{K_c} = 8.5 \pm 2.5\, \rm{m\, s^{-1}}$,respectively. The resulting mass estimates, $\rm{M_b} = 11.7 \pm 5.0\,\rm{M_{\rm \oplus}}$ and $\rm{M_c} = 22.2 \pm 6.7\, \rm{M_{\rm \oplus}}$,suggest that planet b might be less dense, and planet c considerably denserthan previously thought. These results are in tension with the current standardmodels of core-accretion. They suggest that both planets accreted a H/Heenvelope that is smaller than expected, and the trend between the two planets'envelope fractions is the opposite of what is predicted by theory.

One year of AU Mic with HARPS: I -- measuring the masses of the two transiting planets