Evidence that the multiple populations (MPs) are common properties of globular clusters (GCs) is accumulated over the past decades from clusters in the Milky Way and in its satellites. This finding has revived GC research, and suggested that their formation at high redshift must have been a much-more complex phenomenon than imagined before. However, most information on MPs is limited to nearby GCs. The main limitation is that most studies on MPs rely on resolved stars, facing a major challenge to investigate the MP phenomenon in distant galaxies. Here we search for integrated colors of old GCs that are sensitive to the multiple-population phenomenon. To do this, we exploit integrated magnitudes of simulated GCs with MPs, and multi-band Hubble Space Telescope photometry of 56 Galactic GCs, where MPs are widely studied, and characterized as part of the UV Legacy Survey of Galactic GCs. We find that both integrated $C_{rm F275W,F336W,F438W}$ and $m_{rm F275W}-m_{rm F814W}$ colors strongly correlate with the iron abundance of the host GC. In second order, the pseudo two-color diagram built with these integrated colors is sensitive to the MP phenomenon. In particular, once removed the dependence from cluster metallicity, the color residuals depend on the maximum internal helium variation within GCs and on the fraction of second-generation stars. This diagram, which we define here for Galactic GCs, has the potential of detecting and characterizing MPs from integrated photometry of old GCs, thus providing the possibility to extend their investigation outside the Local Group.
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