The role of cluster mass in the multiple populations of Galactic and
  extragalactic globular clusters
  Studies based on Hubble Space Telescope ($HST$) photometry in F275W, F336W,
and F438W have shown that the incidence and complexity of multiple populations
(MPs) in Globular Clusters (GCs) depend on cluster mass. This result, however,
is based on nearby, low-reddening Galactic GCs, for which we can obtain
accurate F275W photometry. In this work we exploit $HST$ photometry in F336W,
F438W, and F814W to characterize MPs in 68 Galactic and extragalactic GCs by
using the pseudo-color $C_{F336W,F438W,F814W}$, which is more efficient in
terms of observation time than the pseudo-color $C_{F275W,F336W,F438W}$ adopted
in previous works. We first analyzed the Galactic GCs alone and find that the
RGB color width strongly correlates with [Fe/H]. After removing the dependence
from metallicity, we obtain a strong correlation with cluster mass, thus
confirming previous findings. We then exploited the RGB width to compare MPs in
Galactic and extragalactic GCs. Similarly to Galactic GCs, the RGB width of
Magellanic Cloud GCs correlates with clusters mass, after removing the
dependence from metallicity. This fact demonstrates that cluster mass is the
main factor affecting the properties of MPs. Magellanic Cloud clusters exhibit,
on average, narrower RGBs than Galactic GCs with similar mass and metallicity.
We suggest that this difference is a signature of stellar mass loss in Galactic
GCs. As an alternative, the mass-RGB-width relation would depend on the host
galaxy. Finally, we used ground-based photometry to investigate Terzan\,7
through the $C_{U,B,I}$ pseudo-color, ground-based analogous of
$C_{F336W,F438W,F814W}$, and find that this cluster is consistent with a simple
population.
