  We test the hypothesis that the sub-millimetre thermal emission and scattered
light gaps seen in recent observations of TW Hya are caused by planet-disc
interactions. We perform global three-dimensional dusty smoothed particle
hydrodynamics simulations, comparing synthetic observations of our models with
dust thermal emission, CO emission and scattered light observations. We find
that the dust gaps observed at 24 au and 41 au can be explained by two
super-Earths ($\sim 4 \mathrm{M}_{\oplus}$). A planet of approximately
Saturn-mass can explain the CO emission and the depth and width of the gap seen
in scattered light at 94 au. Our model produces a prominent spiral arm while
there are only hints of this in the data. To avoid runaway growth and migration
of the planets we require a disc mass of $\lesssim 10^{-2}\,\mathrm{M}_{\odot}$
in agreement with CO observations but 10$-$100 times lower than the estimate
from HD line emission.
