Since 2005, measurements of Collins and Sivers asymmetries from the HERMES and COMPASS experiments have shown that both the transversity and the Sivers PDFs are different from zero and measurable in semi-inclusive DIS on transversely polarised targets. Most of the data were collected on proton targets, and only small event samples were collected in the early phase of the COMPASS experiment on a deuteron (6LiD) target and more recently at JLab, on 3He. As a consequence, the d-quark and the sea-quarks transversity and Sivers PDFs are much more poorly known than those of the u-quark. This constitutes an important limitation to the knowledge of the transverse spin and transverse momentum structure of the nucleon.
The COMPASS Collaboration has proposed to measure semi-inclusive DIS on transversely polarised deuterons with good accuracy, comparable with that of the existing transverse spin asymmetry data on protons. The experiment will take data in 2021, as soon as the CERN long shut-down 2 will be over, providing measurements which will stay unique for many years to come. In particular, the uncertainties on the d-quark transversity PDF is expected to be smaller than the present one by a factor 2 to 4 in the measured x range, and that on the isovector tensor charge of the nucleon will be reduced by a factor of two.