  Polycyclic aromatic hydrocarbon (PAH) emission has long been proposed to be a
potential star formation rate indicator, as it arises from the
photodissociation region bordering the Str\"omgren sphere of young, massive
stars. We apply a recently developed technique of mid-infrared spectral
decomposition to obtain a uniform set of PAH measurements from Spitzer
low-resolution spectra of a large sample of star-forming galaxies spanning a
wide range in stellar mass ($M_\star \approx 10^6-10^{11.4}\,M_{\odot}$) and
star formation rate ($\sim 0.1- 2000\,M_{\odot}\rm\,yr^{-1}$). High-resolution
spectra are also analyzed to measure [Ne II] 12.8 $\mu$m and [Ne III] 15.6
$\mu$m, which effectively trace the Lyman continuum. We present a new relation
between PAH luminosity and star formation rate based on the [Ne II] and [Ne
III] lines. Calibrations are given for the integrated $5-15$ $\mu$m PAH
emission, the individual features at 6.2, 7.7, 8.6, and 11.3 $\mu$m, as well as
several mid-infrared bandpasses sensitive to PAH. We confirm that PAH emission
is suppressed in low-mass, dwarf galaxies, and we discuss the possible physical
origin of this effect.
