Semi - inclusive polarized DIS in terms of Melin moments . I . Polarized

In connection with the semi-inclusive polarized DIS, it is proposed to consider the first Melin moments ∆q of the polarized quark and antiquark densities, instead of the respective variables δq(x), local in Bjorken x themselves. This gives rise to a very essential simplification of the next to leading order (NLO) QCD and, besides, allows one to use the respective QCD sum rules. An expression for ∆ū−∆d̄ in NLO is obtained which is just a simple combination of the directly measured asymmetries and of the quantities taken from the unpolarized data. Investigation of the quark structure of the nucleon is one of most important tasks of modern high energy physics. In this respect deep inelastic scattering (DIS) is of special importance. Thus, the very impressive result of the New Muon Collaboration (NMC) experiment was obtained in 1991, when the unpolarized structure functions of the proton and neutron, F p 2 (x) and F n 2 (x), were precisely measured within a wide range of Bjorken’s x, and, it was established that the integral ∫ 1 0 dx x [F p 2 (x)−F n 2 (x)] does not equal 1/3 (Gottfried sum rule) but has a much smaller value 0.235 ± 0.0026. This means that the densities of u and d sea quarks, ū(x) and d̄(x), in the proton have different values, and ∫ 1 0 dx [d̄(x)− ū(x)] = 0.147± 0.039 6= 0. In polarized DIS, instead of the unpolarized total q = q+ q↓, sea q̄ and valence qV = q− q̄ quark densities, the set of the respective polarized quantities δq(x,Q) = q(x,Q)− q↓(x,Q ), δq̄(x,Q) = q̄(x,Q) − q̄↓(x,Q ) and δqV (x,Q ) = δq(x,Q) − δq̄(x,Q) is the subject of the investigation. So, the question arises: does the polarized sea quark density δq̄ also differ from zero? Recently, a series of theoretical papers appeared ([1-4]) where it was predicted that the quantity δq̄(x,Q) does not equal zero. However, the model-dependent results for δq̄ essentially differ each from other in these papers. So, it is very desirable to find a reliable way to extract this quantity directly from experiment data. For this purpose it is not sufficient to use just the Delivered on October 10 at Physics Workshop ”Compass week in Dubna” (JINR, Dubna, 2000) under the title ”Polarized sea-quark flavor asymmetries and COMPASS.” E-mail address: [email protected] 1 inclusive polarized DIS data, and one has to investigate semi-inclusive polarized DIS processes like ~μ+ ~ p(~ d) → μ+ h +X. Such processes provide direct access to the individual polarized quark and antiquark distributions via measurements of the respective spin asymmetries. 3 Unfortunately, the description of semi-inclusive DIS processes turns out to be much more complicated in comparison with the traditional inclusive polarized DIS. First, the fragmentation functions are involved, for which no quite reliable information is available. Second (and this is the most serious problem), the consideration even of the next to leading (NLO) QCD order turns out to be extremely difficult, since it involves double convolution products. So, to achieve a reliable description it is very desirable, on the one hand, to exclude from consideration the fragmentation functions, whenever possible, and, on the other hand (and this is the main task), to try to simplify the NLO consideration as much as possible, without which one can say nothing about the reliability and stability of results obtained within the quark-parton model (QPM). It is well known (see, for example, [5] and references therein) that within QPM one can completely exclude the fragmentation functions from the expressions for the valence quark polarized distributions δqV through experimentally measured asymmetries. To this end one, instead of the usual virtual photon asymmetry AγN ≡ A h 1N (which is expressed in terms of the directly measured asymmetry Aexp = (n h ↑↓ − n h ↑↑)/(n h ↑↓ + n h ↑↑) as A h 1N = (PBPTfD) Aexp), one has to measure so called ”difference asymmetry” A −h N which is expressed in terms of the respective counting rates as A N (x,Q ; z) = 1 PBPTfD (n↑↓ − n h̄ ↑↓)− (n h ↑↑ − n h̄ ↑↑) (n↑↓ − n h̄ ↑↓) + (n h ↑↑ − n h̄ ↑↑) , (1) where the event densities n↑↓(↑↑) = dN h ↑↓(↑↑)/dz, i.e. n h ↑↓(↑↑)dz are the numbers of events for antiparallel (parallel) orientations of here muon and target nuclear (proton or deutron here) spins for the hadrons of type h registered in the interval dz. Coefficients PB and PT , f and D are the beam and target polarizations, dilution and depolarization factors, respectively,(for details on these coefficients see, for example, [6-7] and references therein). Then, the QPM expressions for the difference asymmetries look like (see, for example, COMPASS project [8], appendix A) A −π p = 4δuV − δdV 4uV − dV ; A −π n = 4δdV − δuV 4dV − uV ; A −π d = δuV + δdV uV + dV ; A −K p = δuV uV ; A −K d = A π−π d , (2) i.e., on the one hand, they contain only valence quark polarized densities, and, on the other hand, have the remarkable property to be free of any fragmentation functions. Such a kind of measurements were performed by SMC and HERMES experiments and are also planned by the COMPASS collaboration. For discussion of this subject see, for example [5] and references therein.