Masses and age of the Chemically Peculiar double-lined binary $\chi$~Lupi

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.