  We aim at measuring the stellar parameters of the two Chemically Peculiar
components of the B9.5Vp HgMn + A2 Vm double-lined spectroscopic binary
HD141556, whose period is 15.25 days. We combined historical radial velocity
measurements with new spatially resolved astrometric observations from
PIONIER/VLTI to reconstruct the three-dimensional orbit of the binary, and thus
obtained the individual masses. We fit the available photometric points
together with the flux ratios provided by interferometry to constrain the
individual sizes, which we compared to predictions from evolutionary models.The
individual masses of the components are $\Ma = 2.84 \pm 0.12\ \Msun$ and $\Mb =
1.94 \pm 0.09\ \Msun$. The dynamical distance is compatible with the Hipparcos
parallax. We find linear stellar radii of $\Ra=2.85 \pm 0.15\ \Rsun$ and
$\Rb=1.75 \pm 0.18\ \Rsun$. This result validates a posteriori the flux ratio
used in previous detailed abundance studies. We determine a sub-solar initial
metallicity $Z=0.012\pm0.003$ and an age of $(2.8\pm0.3)\times10^8\ $years. Our
results imply that the primary rotates more slowly than its synchronous
velocity, while the secondary is probably synchronous. We show that strong
tidal coupling during the pre-main sequence evolution followed by a full
decoupling at zero-age main sequence provides a plausible explanation for these
very low rotation rates.
