  Liller 1 and Terzan 5 are two massive systems in the Milky-Way bulge hosting
populations characterized by significantly different ages ($\Delta t>7-8$ Gyr)
and metallicities ($\Delta$[Fe/H]$\sim1$ dex). Their origin is still strongly
debated in the literature and all formation scenarios proposed so far require
some level of fine-tuning. The detailed star formation histories (SFHs) of
these systems may represent an important piece of information to assess their
origin. Here we present the first attempt to perform such an analysis for
Liller 1. The first key result we find is that Liller 1 has been forming stars
over its entire lifetime. More specifically, three broad SF episodes are
clearly detected: 1) a dominant one, occurred some 12-13 Gyr ago with a tail
extending for up to $\sim3$ Gyr, 2) an intermediate burst, between 6 and 9 Gyr
ago, 3) and a recent one, occurred between 1 and 3 Gyr ago. The old population
contributes to about $70\%$ of the total stellar mass and the remaining
fraction is almost equally split between the intermediate and young
populations. If we take these results at a face value, they would suggest that
this system unlikely formed through the merger between an old globular cluster
and a Giant Molecular Cloud, as recently proposed. On the contrary, our
findings provide further support to the idea that Liller 1 is the surviving
relic of a massive primordial structure that contributed to the Galactic bulge
formation, similarly to the giant clumps observed in star-forming high-redshift
galaxies.

Astrophysics of Galaxies;Solar and Stellar Astrophysics