  We study the impact of baryonic processes and massive neutrinos on weak
lensing peak statistics that can be used to constrain cosmological parameters.
We use the BAHAMAS suite of cosmological simulations, which self-consistently
include baryonic processes and the effect of massive neutrino free-streaming on
the evolution of structure formation. We construct synthetic weak lensing
catalogues by ray-tracing through light-cones, and use the aperture mass
statistic for the analysis. The peaks detected on the maps reflect the
cumulative signal from massive bound objects and general large-scale structure.
We present the first study of weak lensing peaks in simulations that include
both baryonic physics and massive neutrinos (summed neutrino mass $M_{\nu} =$
0.06, 0.12, 0.24, and 0.48 eV assuming normal hierarchy), so that the
uncertainty due to physics beyond the gravity of dark matter can be factored
into constraints on cosmological models. Assuming a fiducial model of baryonic
physics, we also investigate the correlation between peaks and massive haloes,
over a range of summed neutrino mass values. As higher neutrino mass tends to
suppress the formation of massive structures in the Universe, the halo mass
function and lensing peak counts are therefore modified as a function of
$M_{\nu}$. Over most of the S/N range, the impact of fiducial baryonic physics
is greater (less) than neutrinos for 0.06 and 0.12 (0.24 and 0.48) eV models.
Both baryonic physics and massive neutrinos should be accounted for when
deriving cosmological parameters from weak lensing observations.
