  We construct a speculative scenario for rotation-induced extra helium mixing
to the envelope of horizontal branch (HB) stars. This scenario differs from
previous ones in that the mixing occurs after the star has left the red giant
branch (RGB). We follow the evolution of a low metallicity star from the RGB to
the HB, and examine the density profile and radius in the core-envelope
boundary region. In the transition from the RGB to the HB the envelope shrinks
by two orders of magnitude in size and the core swells, such that any
non-negligible rotation on the RGB will result in a strong rotational shear at
the core-envelope boundary. For a non-negligible rotation to exist on the RGB
the star has to be spun up by a companion spiraling inside its envelope (a
common envelope evolution). We speculate that shear instabilities on the HB
might mix helium-rich core material to the envelope. The shallow density
profile on the HB is less likely to prevent mixing. As previously shown, extra
helium mixing can account for the overluminous blue HB stars found in some
globular clusters. Although being speculative, this study supports the idea
that the presence of low mass companions, from planets to low mass main
sequence stars, influence the evolution of stars, and can explain some
properties of the color-magnitude (Herzsprung-Russel) diagram of globular
clusters. Namely, low mass companions can be an ingredient in the so called
`second parameter' of globular clusters.
