  This paper deals with theoretical predictions for He burning models in a
range of masses covering the so-called Red Giant Branch phase transition.
Taking as a guideline the observational constraints given by Hipparcos
parallaxes to the predicted luminosity of models originated from Red Giant
progenitors with He core undergoing electron degeneracy, we compare models by
various authors as recently appeared in the literature, disclosing sensitive
differences in the predicted luminosity. The solidity of these theoretical
predictions is investigated by exploring the effects of varying the assumptions
about the efficiency of core overshooting or the amount of mass loss, giving
quantitative estimates of the related uncertainties. However, one finds that
theoretical predictions concerning the luminosity of the red giant clump in the
Hipparcos sample is scarcely affected by these mechanisms.A comparison among
theoretical predictions as recently given by different authors convincingly
demonstrates that the different luminosity predictions are the natural results
of evolutionary codes with different - but all reasonable- input physics. In
this context observations suggests that stellar models based on the most
updated input physics are possibly overestimating the luminosity of these
structures, raising doubts on several current predictions concerning the
luminosity of HB stars in galactic globulars.
