Transversity in the chiral quark–soliton model and single spin asymmetries

It is well known that three most important (twist-2) elements of the parton density matrix in a nucleon are the non-polarized parton distributions functions (PDF) f1(x), the longitudinal spin distribution g1(x) and the transverse spin distribution (transversity) h1(x) [1]. The first two have been successfully measured experimentally in classical deep inelastic scattering (DIS) experiments but the measurement of the last one is especially difficult since it belongs to the class of the so-called chiral-odd structure functions and can not be seen there. The non-polarized PDF’s have been measured for decades and are rather well known in wide range of x and Q. Their behavior in Q is well described by the QCD evolution equation and serves as one of the main sources of αs(Q ) determination. The longitudinal spin PDF’s drew common attention during last decade in connection with the famous ”Spin Crisis”, i.e. astonishingly small portion of the proton spin carried by quarks (see [2] and references therein). The most popular explanation of this phenomenon is large contribution of the gluon spin ∆G(x). The direct check of this hypothesis is one of the main problems of running dedicated experiments like COMPASS at CERN and RHIC at BNL. Even now, however, there is some indication to a considerable value of ∆G(x) coming from the Q evolution of the polarized PDF’s [3] and from the first direct experimental probe of ∆G(x) by HERMES collaboration [4] with the result ∆G(x)/G(x) = 0.41±0.18 in the region 0.07 < x < 0.28. The latter is in reasonable agreement with large Nc limit prediction [5] ∆G(x)/G(x) ≈ 1/Nc for not very small x. Another problem here is the sea quark spin asymmetry. It is usually assumed in fitting the experimental data that ∆ū = ∆d̄ = ∆s̄. This ad hoc assumption however contradicts with large Nc limit prediction ∆ū ≈ −∆d̄ [5]. This was previously discovered in the instanton model [6] and