  (Abridged) Eclipsing, spectroscopic double-lined binary star systems (SB2)
are excellent laboratories for calibrating theories of stellar interior
structure and evolution. We aim to investigate the mass discrepancy in binary
stars. We study the effect of near-core mixing on the mass of the convective
core of the stars and interpret the results in the context of the mass
discrepancy. Two scenarios are considered, where individual stellar components
of a binary system are treated independent of each other and where they are
forced to have the same age and initial chemical composition. We find that the
mass discrepancy is present in our sample and that it is anti-correlated with
the surface gravity of the star. No correlations are found with other
fundamental and atmospheric parameters, including the stellar mass. The mass
discrepancy can be partially accounted for by increasing the amount of
near-core mixing in stellar evolution models. We also find that ignoring the
microturbulent velocity and turbulent pressure in stellar atmosphere models of
hot evolved stars results in overestimation of their effective temperature by
up to 8%. Together with enhanced near-core mixing, this can almost entirely
account for the 30% mass discrepancy found for the evolved primary component of
V380 Cyg. We find a strong link between the mass discrepancy and the convective
core mass. The mass discrepancy can be solved by considering the combined
effect of extra near-core boundary mixing and consistent treatment in the
spectrum analysis of hot evolved stars. Our binary modelling results in
convective core masses between 17 and 35% of the stellar mass, in excellent
agreement with results from gravity-mode asteroseismology of single stars. This
implies larger helium core masses near the end of the main sequence than
anticipated so far.
