\sigma(\Delta M)}$). Throughout our analysis we will assume that Y varies according to either a uniform probability distribution, from ${\rm Y_{min}}$ to ${\rm Y_{min}+\Delta Y}$, or a Gaussian one. In this latter case ${\rm \Delta Y}$ is the 1$\sigma$ spread around a prescribed mean value. Also for the RGB total mass loss we will assume a Gaussian distribution around the mean value ${\rm \Delta M}$ or a uniform distribution with minimum value equal to ${\rm \Delta M}$. The idea behind this type of simulations (see, e.g., Caloi & D’Antona 2005) is that the colour extension of the HB is driven mainly by the variation of Y rather than mass loss efficiency. A higher initial Y implies a lower mass at the tip of the RGB (for a fixed cluster age) hence, for a fixed value of ${\rm \Delta M}$, a smaller mass along the HB and a bluer colour (the He-core mass is affected by the variation of Y to a smaller extent). Our synthetic HB code first draws randomly a value of Y, and determines the initial mass of the star at the RGB tip (${\rm M_{TRGB}}$) from interpolation among the BaSTI isochrones of the prescribed age. The mass 