We investigate the predicted Color-Magnitude distribution of metal-rich Horizontal Branch ( HB ) stars , discussing selected theoretical models computed under various assumptions about the star metallicity and the efficiency of super-adiabatic convection .
We find that canonical Zero Age Horizontal Branches with metallicity larger or of the order of Z=0.002 should be all affected by a tilt , by an amount which increases when the metallicity is increased and/or the mixing length is decreased , reaching a tilt of \Delta V \sim 0.2 mag in the case of solar metallicity when a mixing length value \alpha =1.6 is assumed ( \Delta V is the magnitude difference between the top of the blue HB and the fainter magnitude reached by the red HB ) .
Uncertainties in the luminosity of the red HB due to uncertainty in the mixing length value are discussed .
We finally discuss the much larger tilt observed in the clusters NGC 6441 and NGC 6388 , reporting additional evidence against suggested non-canonical evolutionary scenarios .
Numerical experiments show that differential reddening could produce such sloped HBs .
Further , HST-PC imaging of NGC 6441 gives clear indications about the occurrence of differential reddening across the cluster .
However , the same imaging shows that the observed slope of the red HB is not an artifact of differential reddening .
We finally show that sloping red HBs in metal rich clusters are a common occurrence not necessarily correlated with the appearance of extended blue HB .