Population synthesis to constrain Galactic and Stellar Physics- I- Determining age and mass of thin-disc red-giant stars

The cornerstone mission Gaia, together with complementary surveys, will revolutionize our understanding of the formation and history of our Galaxy, providing accurate stellar masses, radii, ages, distances, as well as chemical properties for a very large sample of stars across different Galactic stellar populations.Using an improved population synthesis approach and new stellar evolution models we attempt to evaluate the possibility of deriving ages and masses of clump stars from their chemical properties.A new version of the Besancon Galaxy model (BGM) uses new stellar evolutionary tracks computed with STAREVOL.These provide chemical and seismic properties from the PMS to the early-AGB.For the first time, the BGM can explore the effects of an extra-mixing occurring in red-giant stars.In particular we focus on the effects of thermohaline instability on chemical properties as well as on the determination of stellar ages and masses using the surface [C/N] abundance ratio.The impact of extra-mixing on 3He, 12C/13C, N, and [C/N] abundances along the giant branch is quantified.We underline the crucial contribution of asteroseismology to discriminate between evolutionary states of field giants belonging to the Galactic disc.The inclusion of thermohaline instability has a significant impact on 12C/13C,3He as well as on the [C/N] values.We show the efficiency of thermohaline mixing at different metallicities and its influence on the determined stellar mass and age from the observed [C/N] ratio.We then propose simple relations to determine ages and masses from chemical abundances according to these models.We emphasize the usefulness of population synthesis tools to test stellar models and transport processes inside stars.We show that transport processes occurring in red-giant stars should be taken into account in the determination of ages for future Galactic archaeology studies.(abridged)