  Galactic globular clusters (GCs) are known to host multiple stellar
populations: a first generation with a chemical pattern typical of halo field
stars and a second generation (SG) enriched in Na and Al and depleted in O and
Mg. Both stellar generations are found at different evolutionary stages (e.g.,
the main-sequence turnoff, the subgiant branch, and the red giant branch). The
non detection of SG asymptotic giant branch (AGB) stars in several metal-poor
([Fe/H] < -1) GCs suggests that not all SG stars ascend the AGB phase, and that
failed AGB stars may be very common in metal-poor GCs. This observation
represents a serious problem for stellar evolution and GC formation/evolution
theories. We report fourteen SG-AGB stars in four metal-poor GCs (M 13, M 5, M
3, and M 2) with different observational properties: horizontal branch (HB)
morphology, metallicity, and age. By combining the H-band Al abundances
obtained by the APOGEE survey with ground-based optical photometry, we identify
SG Al-rich AGB stars in these four GCs and show that Al-rich RGB/AGB GC stars
should be Na-rich. Our observations provide strong support for present,
standard stellar models, i.e., without including a strong mass-loss efficiency,
for low-mass HB stars. In fact, current empirical evidence is in agreement with
the predicted distribution of FG and and SG stars during the He-burning stages
based on these standard stellar models.
