0 Single Spin Asymmetries in Semi - Inclusive Electroproduction : Access to Transversity

We discuss the quark transversity distribution function and a possible way to access it through the measurement of single spin azimuthal asymmetry in semiinclusive single pion electroproduction on a transversely polarized target. At leading order in 1/Q, the cross section for a hard scattering process is given by the convolution of a hard part and a soft part. The former describes the scattering among elementary constituents and can be calculated perturbatively in the framework of QCD. The latter accounts for the processes in which either partons are produced from the initial hadrons (parton distribution functions) or final hadrons are produced from partons (parton fragmentation functions) which result from the hard elementary scattering. For every quark flavor, besides the well-known parton distribution f1(x) and the longitudinal spin distribution g1(x), there is a third twist-two distribution function, the transversity distribution function h1(x) which was first discussed by Ralston and Soper [1] in double transverse polarized Drell-Yan scattering. The transversity distribution h1(x) measures the probability to find a transversely polarized quark in a transversely polarized nucleon. It is equally important for the description of the spin structure of nucleons as the more familiar function g1(x); their information being complementary. In the non-relativistic limit, where boosts and rotations commute, h1(x) = g1(x); then difference between these two functions may turn out to be a measure for the relativistic effects within nucleons. On the other hand, there is no gluon analog on h1(x). This may have interesting consequences for ratios of transverse to longitudinal asymmetries in polarized hard scattering processes (see e.g. Ref. [2]). The transversity distribution h1(x) remains still unmeasured. The reason is that 1) E-mail: [email protected] it is a chiral odd function, and consequently it is suppressed in inclusive deep inelastic scattering (DIS) [3]. Since electroweak and strong interactions conserve chirality, h1(x) cannot occur alone, but has to be accompanied by a second chiral odd quantity. In principle, transversity distributions can be extracted from cross section asymmetries in polarized processes involving a transversely polarized nucleon. In the case of hadron-hadron scattering these asymmetries can be expressed through a flavor sum involving a product of two chiral-odd transversity distributions. This is one of the main goals of the spin program at RHIC [4]. An evaluation of the corresponding asymmetry was carried out [5] by assuming the saturation of Soffer’s inequality [6] for the transversity distribution: the maximum possible asymmetry at RHIC energies was estimated to be about 2%. At smaller energies ( √ s ≃ 40 GeV), e.g. for a possible fixed-target hadron-hadron spin experiment at the proposed HERA~ N facility [7] the asymmetry is expected to be higher (about 4%). In the case of semi-inclusive deep inelastic lepton scattering (SIDIS) off transversely polarized nucleons there exist several methods to access transversity distributions. One of them, the twist-3 pion production [8], uses longitudinally polarized leptons and measures a double spin asymmetry. The other methods do not require a polarized beam, and rely on the polarimetry of the scattered transversely polarized quark. They consist on: • the measurement of the transverse polarization of Λ’s in the current fragmentation region [9,10], • the observation of a correlation between the transverse spin vector of the target nucleon and the normal to the two-meson plane [11,12], • the observation of the “Collins effect” in quark fragmentation through the measurement of pion single target-spin asymmetries [13–15]. In the following we will mainly focus on the last method. To access the transversity in SIDIS off transversely polarized nucleons, one can measure the azimuthal angular dependences in the production of spin-0 or (on average) unpolarized hadrons. This production is described by the intrinsic transverse momentum dependent fragmentation function H 1 (z) which is also chiral odd and, moreover, T-odd, i.e., non-vanishing only due to final state interactions. Collins [13] was the first to propose such a spin dependent fragmentation function. It can be obtained, for example, in two-hadron production in ee annihilation [16]. In the cross section of SIDIS off transversely polarized nucleons it shows up as a sin(φh + φS) dependence, where φh is the azimuthal angle of the outgoing hadron (with non-zero transverse momentum PhT ) around the virtual-photon direction, and φS is the azimuthal angle of the target spin vector, both in relation to the lepton scattering plane. 2) The relevant kinematics is: Q = −q2 where q = k1 − k2, k1 (k2) being the 4-momentum of the incoming (outgoing) charged lepton is the 4-momentum of the virtual photon. P (Ph) is the momentum of the target (final hadron), x = q/2(Pq), y = (Pq)/(Pk1), z = (PPh)/(Pq) The sin(φh+φS) moment in the SIDIS cross-section can be related to the parton distribution and fragmentation functions involved in the parton level description of the underlying process [14,15]. This moment is defined as the appropriately weighted integral over PhT (the transverse momentum of the observed hadron) of the cross section asymmetry: 〈 |PhT | Mh sin(φh + φS)〉UT ≡ ∫ dPhT |PhT | Mh sin(φh + φS) (