Context. In this paper we present multiband optical and UV Hubble Space Telescope photometry of the two Galactic globular clusters NGC 6388 and NGC 6441.
Aims. We investigate the properties of their anomalous horizontal branches in different photometric planes in order to shed light on the nature of the physical mechanism(s) responsible for the existence of an extended blue tail and of a slope in the horizontal branch, visible in all the color-magnitude diagrams.
Methods. New photometric data have been collected and carefully reduced. Empirical data have been compared with updated stellar models of low-mass, metal-rich, He-burning structures, transformed to the observational plane with appropriate model atmospheres.
Results. We have obtained the first UV color-magnitude diagrams for NGC 6388 and NGC 6441. These diagrams confirm previous results, obtained in optical bands, about the presence of a sizeable stellar population of extremely hot horizontal branch stars. At least in NGC 6388, we find a clear indication that at the hot end of the horizontal branch the distribution of stars forms a hook-like feature, closely resembling those observed in NGC 2808 and Omega Cen. We briefly review the theoretical scenarios that have been suggested for interpreting this observational feature. We also investigate the tilted horizontal branch morphology and provide further evidence that supports early suggestions that this feature cannot be interpreted as an effect of differential reddening. We show that a possible solution of the puzzle is to assume that a small fraction - ranging between 10-20% - of the stellar population in the two clusters is strongly helium-enriched (Y ~ 0.40 in NGC 6388 and Y ~ 0.35 in NGC 6441). The occurrence of a spread in the He abundance between the canonical value (Y ~ 0.26) and the quoted upper limits can significantly help in explaining the "whole" morphology of the horizontal branch and the pulsational properties of the variable stars in the target clusters
