On the Parton Interpretation of Quark Fragmentation into Hadrons with Different Spins

We calculate the spin density matrix of the hadron $h$ created via quark fragmentation in the process $e^-e^+ \to q\bar q \to h + X$. In the case of $h=\Lambda$ the experimental data could possibly elucidate the problem of $s$-quark contribution to the spin of the $\Lambda$-hyperon, to be compared with the case of the proton (``spin crisis''). Generally we find that for hadrons with spin 1/2 the parton description, using only probabilities, works much better than for vector particles, since in the former case the non diagonal matrix elements of the hadron spin density matrix are suppressed by a small factor $p_T/(z\sqrt s)$, where $p_T$ is the hadron transverse momentum inside the jet.