Time-reversal odd distribution functions in leptoproduction

Abstract

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-

Nucleon structure from generalized parton distributions in lattice QCD

“…(18) also leads to a strong transverse deformation orthogonal to the transverse quark spin for an unpolarized nucleon. According to [15], this distortion in +y-direction 3 due to the transversely polarized quarks may correspond to a non-zero, negative Boer-Mulders function [25] h ⊥ 1 < 0 for up-quarks. For the plot on the RHS in Fig.…”

Azimuthal and single spin asymmetries in hard scattering processes

“…No significant cos 2φ dependence was found, in contrast with pion-induced DY data discussed above. These results put constraints on theoretical models that predict a large cos 2φ dependence originating from QCD vacuum effects and suggest that the sea-quark Boer-Mulders functions [108] are much smaller than those for valence quarks.…”

“…[126,108]. For the twist-three case these functions have no partonic interpretation since they are related to quark-quark-gluon matrix elements.…”

“…[108]); 3) The combinations F ++ +− ± F −− +− are respectively related to the probability of finding an unpolarized (longitudinally polarized) quark inside a transversely polarized hadron, that is to the well-known Sivers function [18,19] …”

Evolution of the helicity and transversity. Transverse-momentum-dependent parton distributions

“…For the description of a spin-1/2 target, eight independent TMDs can be introduced (at leading twist) [22][23][24][25]. At present, there exist explicit formulas for the evolution of two of them: the unpolarized TMD, f 1 (x, k T ), and the Sivers function, f ⊥ 1T (x, k T ).…”