COMPASS results on Transverse single-spin asymmetries

New results on single spin asymmetries of charged hadrons produced in deep-inelastic scattering of muons on a transversely polarised LiD target are presented. The data were taken in the years 2002, 2003 and 2004 with the COMPASS spectrometer using the muon beam of the CERN SPS at 160 GeV/c. Preliminary results are given for the Sivers asymmetry and for all the three ``quark polarimeters'' presently used in COMPASS to measure the transversity distributions. The Collins and the Sivers asymmetries for charged hadrons turn out to be compatible with zero, within the small (~1%) statistical errors, at variance with the results from HERMES on a transversely polarised proton target. Similar results have been obtained for the two hadron asymmetries and for the Lambda polarisation. First attempts to describe the Collins and the Sivers asymmetries measured by COMPASS and HERMES allow to give a consistent picture of these transverse spin effects.