Semi-inclusive Hadron-hadron Transverse Spin Asymmetries and Their Implication for Polarized Dis

We discuss 1 a possible explanation of the 25 year old mystery of the large transverse spin asymmetries found in many semi-inclusive hadron-hadron reactions. We obtain the first reliable information about the transverse polarized quark densities ∆T q(x) and we find surprising implications for the usual, longitudinal, polarized DIS. The plan of the presentation is as follows: 1) A brief reminder about the internal structure of the nucleon. 2) The transverse asymmetries. 3) Why it is so difficult to explain the asymmetries. 4) Failure and then success using a new soft mechanism. 5) implications for polarized DIS. Presented by E. Leader 1 Internal structure of the nucleon at the parton level For each quark there are three kinds of number densities: a) The usual q(x) p = xP P q(x) is the number density of quarks with momentum fraction in the range x ≤ p/P ≤ x+∆x. This is mostly measured in DIS. b) The longitudinal polarized density ∆q(x) p = xP P S s (-) (+) or q±(x) is the number density at x with spin s along (+) or opposite (-) to the spin S (=⇒) of the nucleon. The new density is ∆q(x) = q+(x)− q−(x) . (1) It is measured in DIS using a longitudinally polarized nucleon target. c) The transverse polarized density ∆T q(x) p = xP P S s or q↑↓(x) are the number densities at x with transverse spin s along (↑) or opposite (↓) to the transverse nucleon spin S (⇑). The new density is ∆T q(x) = q↑(x)− q↓(x) . (2) Note that ∆T q(x) cannot be measured in DIS with a transversely polarized target; g2(x) does not tell us anything about ∆T q(x). In summary there are 3 independent functions, all equally fundamental, describing the internal structure of the nucleon: q(x), ∆q(x) and ∆T q(x). How can we measure ∆T q(x) ? The ideal reaction would be Drell-Yan using transversely polarized beam and target, but this has never been done. It is one of the prime aims at RHIC. Can one use semi-inclusive hadron-hadron reactions with a transversely polarized target ? At first sight, yes. At second sight, no. And finally, yes, but one has to introduce a new theoretical idea and thereby it seems possible to resolve the ancient puzzle of the large transverse spin asymmetries. 2 The transverse spin asymmetries There is a mass of data on reactions of the type A + B → C + X for which the asymmetry AN under the reversal of the transverse spin is measured: AN = dσ − dσ dσ⇑ + dσ⇓ . (3) Some examples are shown in Fig. 1 for pp → πX and pp → πX 1) respectively. From looking at many reactions one concludes that: – the asymmetries are large ! – they increase with pT – they increase with xF – they seem independent of energy – they occur in a variety of reactions. For decades there has been no serious theoretical explanation and, as we shall see, the standard approach via perturbative QCD gives AN = 0. -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0 0.2 0.4 0.6 0.8 1 A