Transversity and $Lambda$ polarization at COMPASS

The study of Λ polarization in Semi-Inclusive Deep Inelastic Scattering (SIDIS) with a transversely polarized target has often been suggested as a privileged way to access transversity, as the initial quark polarization can be transmitted to the hyperon and then observed via its weak decay. COMPASS measured the Λ transversity-induced polarization as a function of Bjorken x, of the fraction z of the longitudinal momentum of the fragmenting quark carried by the Λ and of the Λ transverse momentum PT. The results are compatible with zero in all regions of phase space. Under the hypothesis that transversity is a valence object, the previous knowledge of the transversity function allows to get information on the ratio of polarized and unpolarized z−integrated Λ fragmentation functions. On the other hand, if the Λ polarization is entirely due to the s quark, or if a quark-diquark model is applied, information can be obtained on the s quark transversity function.