  Low-loss deposited dielectrics are beneficial for the advancement of
superconducting integrated circuits for astronomy. In the microwave band
($\mathrm{\sim}$1$\unicode{x2013}$10 GHz) the cryogenic and low-power
dielectric loss is dominated by two-level systems. However, the origin of the
loss in the millimeter-submillimeter band ($\mathrm{\sim}$0.1$\unicode{x2013}$1
THz) is not understood. We measured the loss of hydrogenated amorphous SiC
(a-SiC:H) films in the 0.27$\unicode{x2013}$100 THz range using superconducting
microstrip resonators and Fourier-transform spectroscopy. The agreement between
the loss data and a Maxwell-Helmholtz-Drude dispersion model suggests that
vibrational modes above 10 THz dominate the loss in the a-SiC:H above 200 GHz.
