Time-reversal odd distribution functions in leptoproduction

In this paper we study the effects of the possible presence of time-reversal ~T! 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 @1#. 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 @2#. This allows so-called T-odd quantities, although it is hard to say something about their magnitude. In Ref. @3# 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 @4#. 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 @1#. For the distribution functions, it has been conjectured that T-odd quantities also might appear without violating time-reversal invariance @5– 8#. This might be due to soft initial state interactions or, as suggested recently @8#, be a consequence of chiral symmetry breaking. Within QCD a possible description of the effects may come from gluonic poles @9#. It is convenient to use the hadron momenta in the process lH→l8hX to define two lightlike vectors n1 and n2 , satis-