  We herein determine the average integrated mass loss from stars stars
belonging to the dominant metal-poor population ([Fe/H] ~ --1.7) of the
Galactic globular cluster omega Centauri (NGC 5139) during their red giant and
horizontal branch evolution. Masses are empirically calculated from
spectroscopic measurements of surface gravity and photometric measurements of
temperature and luminosity. Systematic uncertainties prevent an absolute
measurement of masses at a phase of evolution. However, the relative masses of
early asymptotic giant branch stars and central red giant branch stars can be
measured, and used to derive the mass loss between these two phases. This can
then be used as a physical check of models of horizontal branch (HB) stars. For
omega Cen, the average difference is found to be 26 +/- 4%. Assuming initial
and final masses of 0.83 and 0.53 solar masses, we determine that 0.21 +/- 0.03
solar masses is lost on the RGB and 0.09 +/- ~0.05 solar masses is lost on the
AGB. The implied HB stellar mass of 0.62 +/- 0.04 solar masses is commensurate
with literature determinations of the masses of the cluster's HB stars. The
accuracy of this measurement can be improved through better selection of stars
and spectral coverage, and applied to other clusters where horizontal branch
models do not currently agree.
