  New millimeter-wave CO and HCN observations of the host galaxies of
infrared-excess Palomar Green quasi-stellar objects (PG QSOs) previously
detected in CO are presented. These observations are designed to assess the
validity of using the infrared luminosity to estimate star formation rates of
luminous AGN by determining the relative significance of dust-heating by young,
massive stars and active galactic nuclei (AGN) in QSO hosts and IRAS galaxies
with warm, AGN-like infrared colors. The HCN data show the PG QSO host IZw1 and
most of the warm IRAS galaxies to have high L_IR / L'_HCN (>1600) relative to
the cool IRAS galaxy population for which the median L_IR / L'_HCN ~
890(+440,-470). If the assumption is made that the infrared emission from cool
IRAS galaxies is reprocessed light from embedded star-forming regions, then
high values of L_IR / L'_HCN are likely the result of dust heating by the AGN.
Further, if the median ratio of L'_HCN / L'_CO ~ 0.06 observed for Seyfert
galaxies and IZw1 is applied to the PG QSOs not detected in HCN, then the
derived L_IR / L'_HCN correspond to a stellar contribution to the production of
L_IR of ~ 7-39%, and star formation rates ~ 2-37 M_sun/yr are derived for the
QSO hosts. Alternatively, if the far-infrared is adopted as the star formation
component of the total infrared in cool galaxies, the stellar contributions in
QSO hosts to their L_FIR are up to 35% higher than the percentages derived for
L_IR. This raises the possibility that the L_FIR in several of the PG QSO
hosts, including IZw1, could be due entirely to dust heated by young, massive
stars. Finally, there is no evidence that the global HCN emission is enhanced
relative to CO in galaxies hosting luminous AGN.
