  Accurate knowledge of the effect of feedback from galaxy formation on the
matter distribution is a key requirement for future weak lensing experiments.
Recent studies using hydrodynamic simulations have shown that different
baryonic feedback scenarios lead to significantly different two-point shear
statistics. In this paper we extend earlier work to three-point shear
statistics. We show that, relative to the predictions of dark matter only
models, the amplitude of the signal can be reduced by as much as 30-40% on
scales of a few arcminutes. We find that baryonic feedback may affect two- and
three-point shear statistics differently and demonstrate that this can be used
to assess the fidelity of various feedback models. In particular, upcoming
surveys such as Euclid might be able to discriminate between different feedback
models by measuring both second- and third-order statistics. Because it will
likely remain impossible to predict baryonic feedback with high accuracy from
first principles, we argue in favour of phenomenological models that can
capture the relevant effects of baryonic feedback processes in addition to
changes in cosmology. We construct such a model by modifying the dark
matter-only halo model to characterise the generic effects of energetic
feedback using a small number of parameters. We use this model to perform a
likelihood analysis in a simplified case in which two- and three-point shear
statistics are measured between 0.5 and 20 arcmin and in which the amplitude of
fluctuations, sigma8, the matter density parameter, Om, and the dark energy
parameter, w0, are the only unknown free parameters. We demonstrate that for
weak lensing surveys such as Euclid, marginalising over the feedbac parameters
describing the effects of baryonic processes, such as outflows driven by
feedback from star formation and AGN, may be able to mitigate the bias
affecting Om, sigma8 and w0.
