Dftt 61/95 Infnca-th9526

We discuss the production of hadrons in polarized lepton nucleon interactions and in the current jet fragmentation region; using the QCD hard scattering formalism we compute the helicity density matrix of the hadron and show how its elements, when measurable, can give information on the spin structure of the nucleon and the spin dependence of the quark fragmentation process. The cases of ρ vector mesons and Λ baryons are considered in more details and, within simplifying assumptions, some estimates are given. 1 Introduction and general formalism The full description of hard scattering processes involving hadrons always requires a knowledge of both the elementary interactions between the hadronic constituents and the constituent distribution or fragmentation properties; while the former interactions are computable in perturbative QCD or QED the latter properties, i.e. the amount of quarks and gluons inside hadrons and the amount of observed particles resulting from a quark or gluon fragmentation, are non perturbative and cannot be computed in QCD. However, their universality and the QCD knowledge of their Q evolution allow, once some information is obtained from certain processes, to use it in other processes in order to make genuine predictions. It is then crucial to collect phenomenological information on these non perturbative quantities. On the quark and gluon content of the nucleons we have by now gathered plenty of detailed information mainly from unpolarized Deep Inelastic lepton-nucleon Scattering; some information is also available on unpolarized quark fragmentation properties either from DIS or ee annihilations. Much less we know about the inner structures of polarized hadrons and their dynamical properties. The proton and neutron spin structure functions have recently received much attention and their improved measurements have caused great surprise and enormous theoretical activity [1], but we still need a better knowledge; very little is known on polarized quark and gluon fragmentations. Several observed spin effects are not well understood and are certainly related to non perturbative hadronic properties. We consider here the inclusive deep inelastic process lN → hX (1) in which an unpolarized or polarized lepton scatters off a polarized nucleon and one observes a final hadron h whose spin state is studied through the measurement of its helicity density matrix ρ(h). The incoming lepton interacts with a polarized quark inside the polarized nucleon and the quark then fragments into the hadron h contributing to its spin; thus, we expect to learn something on the polarized quark distribution and fragmentation functions. We consider spin 1 and spin 1/2 final hadrons and different polarizations of the initial nucleon; we consider either unpolarized or longitudinally polarized leptons because, as we shall see, transversely polarized ones cannot add any further information. According to the QCD hard scattering scheme and the factorization theorem [2][4], [5] the helicity density matrix of the hadron h inclusively produced in reaction (1) is given by ρ (s,S) λ h ,λ h (h) Eh d σ dph = ∑ q;λ l ,λq,λ ′ q ∫ dx πz 1 16πx2s2 (2) ρ λ l ,λ l ρ q/N,S λq ,λ ′ q fq/N(x) M̂ q λ l ,λq;λl,λq M̂ q∗ λ l ,λ′q;λl,λ ′ q D λq,λ ′ q λ h ,λ h (z) where ρ is the helicity density matrix of the initial lepton with spin s, fq/N (x) is the number density of unpolarized quarks q with momentum fraction x inside an 1 unpolarized nucleon and ρ is the helicity density matrix of quark q inside the polarized nucleon N with spin S. The M̂ q λ l ,λq;λl,λq ’s are the helicity amplitudes for the elementary process lq → lq. The final lepton spin is not observed and helicity conservation of perturbative QCD and QED has already been taken into account in the above equation: as a consequence only the diagonal elements of ρ contribute to ρ(h) and non diagonal elements, present in case of transversely polarized leptons, do not contribute. D λq,λ ′ q λ h ,λ h (z) is the product of fragmentation amplitudes D λq,λ ′ q λ h ,λ h (z) = ∑ ∫ X,λ X Dλ X ,λh;λq D λX ,λ′h;λ′q (3)