  While it is established that the pinch point scattering pattern in spin ice
arises from an emergent coulomb phase associated with magnetic moment that is
divergence-free, more complex Hamiltonians can introduce a divergence-full
part. If these two parts remain decoupled, they give rise to the co-existence
of distinct features. Here we show that the moment in ${\rm Nd_2Hf_2O_7}$ forms
a static long-range ordered ground state, a flat, gapped pinch point excitation
and dispersive excitations. These results confirm recent theories which predict
that the dispersive modes, which arise from the divergence-full moment, host a
pinch point pattern of their own, observed experimentally as `half-moons'.
