Spin effects in the fragmentation of transversely polarized and unpolarized quarks

We study the fragmentation of a transversely polarized quark into a non collinear (k_T not= 0) spinless hadron and the fragmentation of an unpolarized quark into a non collinear transversely polarized spin 1/2 baryon. These nonperturbative properties are described by spin and k_T dependent fragmentation functions and are revealed in the observation of single spin asymmetries. Recent data on the production of pions in polarized semi-inclusive DIS and long known data on Lambda polarization in unpolarized p-N processes are considered: these new fragmentation functions can describe the experimental results and the single spin effects in the quark fragmentation turn out to be surprisingly large.