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We are studying mass loss in red giant branch (RGB) stars with mass $< 1.1 M_\odot$ for the range of metallicities [Fe/H] = $-$2.26 to 0.37. The aim is twofold: (1) Is it possible to find a mass loss law that will produce substantial extreme horizontal branch (EHB) populations? This is important because several studies have suggested that EHB stars and their progeny contribute considerably to the UVX phenomenon in elliptical galaxies and spiral bulges. (2) Can strong RGB mass loss explain the stars observed to lie below the expected zero$-$age horizontal branch (ZAHB) in $\omega$ Centauri (Whitney et al.,~1994)? Mass loss causes stars to ``peel$-$off'' the RGB and increase in temperature at constant luminosity before settling on the white dwarf (WD) cooling curve. Under certain conditions the RGB peel$-$off stars ignite helium while on the WD cooling curve. As ZAHB stars, these peel$-$off stars would be dimmer than normal ZAHB stars and could possibly explain the unusually faint $\omega$ Cen stars.
We have incorporated a treatment of mass loss into our stellar evolution code. Mass loss, using the Reimers' formalism, was assumed to occur during the RGB phase. We find that peel-off stars undergo the helium flash over a fairly large range of the Reimers' efficiency parameter $\eta_R$, at a given metallicity. Flashing peel$-$off stars will form EHB stars. The range of $\eta_R$ corresponding to these EHB stars is typically $\sim 0.7 - 0.85$ and is comparable to the range needed to produce a normal HB. Hence it is possible to generate EHB stars using Reimers' formula. From ZAHB models for these stars, we find that the ZAHB of the peel$-$off stars has a spread in luminosity at constant temperature, at the blue end of the normal ZAHB. Ensuing AGB$-$Manqu\'{e} evolution of these stars will produce a roughly vertical sequence of stars starting 0.1 magnitude below the normal ZAHB. Future work will relate this to the $\omega$ Cen observations.
