Double–spin Transverse Asymmetries in Drell–yan Processes

We calculate the double–spin transverse asymmetries for the Drell–Yan lepton pair production in pp and p̄p collisions. We assume the transverse and the longitudinal polarization densities to be equal at a very small scale, as it is suggested by confinement model results. Using a global fit for the longitudinal distributions, we find transverse asymmetries of order of 10 at most, in the accessible kinematic regions. Typeset using REVTEX 1 The transverse polarization distribution of quarks (or antiquarks) h 1 (x,Q ), originally introduced by Ralston and Soper [1] and studied in more detail in recent years [2–4], is totally unknown from an experimental viewpoint. The reason is that h1 is a chirally odd quantity [2] and hence cannot be measured in deep inelastic scattering. The best way to determine h1 is by pp or, at least in principle, p̄p collisions with two transversely polarized beams . The measurement of h1 in proton–proton collisions is now a chapter of the physics program of the STAR and PHENIX experiments at RHIC [6] and of the proposed HERA~ N experiment at HERA [7]. A careful analysis of the theoretical situation is therefore called for. What is planned to be measured is the double–spin transverse asymmetry, whose operational definition is ATT = dσ↑↑ − dσ↑↓ dσ↑↑ + dσ↑↓ , (1) where the arrows denote the transverse directions along which the two colliding hadrons are polarized. Among the processes initiated by pp scattering one can make a selection choosing those which are expected to yield the largest ATT . In fact, since there is no analogue of h1 for gluons [2], all processes taking place at the partonic level via qg or gg scattering give a large contribution to the denominator of (1) and a vanishing one to the numerator, thus producing a negligibly small ATT [8,9]. This leaves us with only one promising reaction: the Drell-Yan lepton pair production. The double–spin transverse asymmetry for this process was calculated in [8,10,11] and found to be relatively large (∼ 0.1 − 0.3 at √s = 100 GeV and for a dilepton mass M = 10 GeV). The basic assumption made in Refs. [8,10] in order to calculate ATT was that h q 1 and h q̄ 1 are equal to the helicity distributions ∆q and ∆q̄, Also semiinclusive reactions would allow extracting h1 but these processes are theoretically more complicated as they involve combinations of twist–3 distributions and unknown fragmentation functions [5].