  We report the results of an inelastic X-ray scattering study of the lattice
dynamics in the paraelectric phase of the antiferroelectric lead hafnate
PbHfO$_3$. The study reveals an avoided crossing between the transverse
acoustic and transverse optic phonon modes propagating along the [1 1 0]
direction with [1 -1 0] polarization. The static susceptibility with respect to
the generally incommensurate modulations is shown to increase on cooling for
the entire $\Gamma$-M direction. We consider different approaches to the data
analysis that correspond to different models for the temperature evolution of
the dynamic susceptibility function. A number of similarities and differences
between the lattice dynamics of PbHfO$_3$ and PbZrO$_3$ are described.
