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)
