We consider the various asymmetries, notably single spin asymmetries, that appear in leptoproduction as a consequence of the presence of time-reversal odd distribution functions. This could facilitate experimental searches for time-reversal odd phenomena. ͓S0556-2821͑98͒02709-X͔ PACS number͑s͒: 13.85. Ni, 13.87.Fh, 13.88.ϩe In this paper we study the effects of the possible presence of time-reversal ͑T͒ odd distribution functions in leptoproduction. We limit ourselves to the production of hadrons in the current fragmentation region, for which we assume that the cross section factorizes into a product of a distribution function and a fragmentation function. Including the effects of transverse momenta, the cross section is assumed to factorize into a convolution of distribution and fragmentation functions which not only depends on the light-cone momentum fractions of quark and hadron, but also on the transverse momentum of quark with respect to hadron or vice versa ͓1͔.Starting with the expressions of the soft parts in hard scattering processes as quark-quark light-front correlation functions, i.e. matrix elements of nonlocal combinations of quark fields, one can analyze the various possible distribution and fragmentation functions. Constraints arise from Lorentz invariance, Hermiticity, parity invariance and time-reversal invariance. The latter, however, cannot be used as a constraint on fragmentation functions, because the produced hadron can interact with the debris of the fragmenting quark, a wellknown phenomenon in any decay process ͓2͔. This allows so-called T-odd quantities, although it is hard to say something about their magnitude. In Ref. ͓3͔ it was even conjectured that final state interaction phases average to zero for single hadron production after summation over unobserved final states.Without considering transverse momenta of quarks, the T-odd effects are higher twist, appearing at order 1/Q ͓4͔. Including transverse momenta of quarks, there are leading order effects. One can have fragmentation of transversely polarized quarks into unpolarized or spin zero hadrons or production of transversely polarizated hadrons in the fragmentation of unpolarized quarks ͓1͔. For the distribution functions, it has been conjectured that T-odd quantities also might appear without violating time-reversal invariance ͓5-

We study the cross section for one-particle inclusive deep inelastic scattering off the nucleon for low transverse momentum of the detected hadron. We decompose the cross section in terms of structure functions and calculate them at tree level in terms of transverse-momentum-dependent parton distribution and fragmentation functions. Our results are complete in the one-photon exchange approximation at leading and first subleading twist accuracy, with both beam and target polarization.

We analyze the transverse-momentum-dependent distribution and fragmentation functions in space-like and time-like hard processes involving at least two hadrons, in particular, 1-particle inclusive leptoproduction, the Drell-Yan process and two-particle inclusive hadron production in electron-positron annihilation. As is well known, transverse momentum dependence allows for the appearance of unsuppressed single spin azimuthal asymmetries, such as Sivers and Collins asymmetries. Recently, Belitsky, Ji and Yuan obtained fully color-gauge-invariant expressions for the relevant matrix elements appearing in these asymmetries at leading order in an expansion in the inverse hard scale. We rederive these results and extend them to observables at the next order in this expansion. We observe that at leading order one retains a probability interpretation, contrary to a claim in the literature and show the direct relation between the Sivers effect in single spin asymmetries and the Qiu-Sterman mechanism. We also study fragmentation functions, where the process-dependent gauge link structure of the correlators is not the only source of T-odd observables and discuss the implications for universality.

The complete tree-level result up to order 1/Q for polarized deep-inelastic leptoproduction [Nucl. Phys. B461 (1996) We present the results of the tree-level calculation of deep-inelastic leptoproduction, including polarization of target hadron and produced hadron. We also discuss the dependence on transverse momenta of the quarks, which leads to azimuthal asymmetries for the produced hadrons.

The representation of quark distribution and fragmentation functions in terms of nonlocal operators is combined with a simple spectator model. This allows us to estimate these functions for the nucleon and the pion ensuring correct crossing and support properties. We give estimates for the unpolarized functions as well as for the polarized ones and for subleading (higher twist) functions. Furthermore we can study several relations that are consequences of Lorentz invariance and of C, P, and T invariance of the strong interactions. PACS number(s): 13.60. Hb, 12.38.Lg, 13.87.Fh