Review of SSA results on deuteron at COMPASS

The measuring of transverse single spin asymmetries (SSA) is part of the physics program at COMPASS, a fixed target experiment at CERN SPS. In 2002-04 the COMPASS experiment has collected data with a transversely polarised $^{6}$LiD target using a 160 GeV/c polarised $\mu^{+}$ beam. By measuring transverse SSA one has access to the transversity distribution function $\Delta_{T}q(x)$. This is one of the three quark distribution functions, which are needed to fully describe the spin structure of the nucleon at leading twist. At COMPASS three different quark polarimeters have been used to access transversity: the Collins effect, which produces an azimuthal asymmetry in the single hadron distribution, the azimuthal target spin asymmetries of charged hadron pairs and the transverse polarisation of $\Lambda$ hyperons. In addition the SSA arising from the correlation between the transverse nucleon spin and the quark intrinsic transverse momentum (Sivers effect), was measured, together with six more transverse target spin asymmetries. All the asymmetries measured on the deuteron target are small and compatible with zero.