  The power spectrum has been a workhorse for cosmological studies of
large-scale structure. However, the present-day matter distribution is highly
non-Gaussian and significant cosmological information is also contained in
higher-order correlation functions. Meanwhile, baryon physics (particularly AGN
feedback) has previously been shown to strongly affect the two-point statistics
but there has been limited exploration of its effects on higher-order functions
to date. Here we use the BAHAMAS suite of cosmological hydrodynamical
simulations to explore the effects of baryon physics and massive neutrinos on
the halo bispectrum. In contrast to matter clustering which is suppressed by
baryon physics, we find that the halo clustering is typically enhanced. The
strength of the effect and the scale over which it extends depends on how
haloes are selected. On small scales (k > 1 $h$ Mpc$^{-1}$, dominated by
satellites of groups/clusters), we find that the bispectrum is highly sensitive
to the efficiency of star formation and feedback, making it an excellent
testing ground for galaxy formation models. We show that the effects of
feedback and the effects of massive neutrinos are largely separable
(independent of each other) and that massive neutrinos strongly suppress the
halo bispectrum on virtually all scales up to the free-streaming length (apart
from the smallest scales, where baryon physics dominates). The strong
sensitivity of the bispectrum to neutrinos on the largest scales and galaxy
formation physics on the smallest scales bodes well for upcoming precision
measurements from the next generation of wide-field surveys.
