Globular cluster archaeology: Hydrogen-burning nucleosynthesis and extra mixing in extinct stars

We compute the evolution of the surface CNO abundances in two types of stars that might have contributed to the star-to-star abundance variations in globular clusters: intermediate-mass asymptotic giant branch stars and low-mass upper red giant branch stars. We show that abundances of [C/Fe] less than or similar to -1 accompanied by apparent signatures of oxygen processing, such as very high [N/Fe] or negative [O/Fe], as observed in some of the globular cluster subgiants and red giants, cannot originate from hot-bottom burning in intermediate-mass asymptotic giant branch stars. This is a robust nucleosynthesis prediction. At the same time, such peculiar CNO abundances could come from the vicinity of the hydrogen-burning shell in upper red giant branch stars, provided that some of them had experienced enhanced extra mixing in the past themselves.