On the Determination of Spin–Dependent Parton Distributions in Semi–Inclusive Deep Inelastic Scattering

New polarized fragmentation functions are introduced and justified, in addition to those conventional ones assumed to be independent of the helicity of the parent parton. It is demonstrated that due to our present ignorance concerning these new parton–spin dependent leading–twist fragmentation functions, it is impossible to utilize current experiments on spin–dependent semi–inclusive deep inelastic lepton nucleon scattering to disentangle the separate polarized parton distributions. Semi–inclusive deep inelastic scattering (SIDIS) in, say, ep → ehX reactions depends on the parton distributions in the proton, f(x,Q) = u, ū, d, d̄, . . . , as well as on their fragmentation functions D f (z,Q ) into the (unpolarized) hadron h (= π, K dominantly). A common assumption [1] concerning the fragmentation functions is their mere dependence on f irrespective of its origin. This, however, needs not necessarily hold true. Considering, for example, a proton with helicity + 2 and its partons with positive and negative helicities f±(x,Q ). It may well be that D f+(z,Q ) 6= D f−(z,Q ) due to the different helicities of the remnant spectator core relative to the fragmenting parton. These different relative helicities could influence the formation of the hadronic shower responsible for the hadronic D f±(z,Q ), especially in the small–z region, as obtained from input distributions D f±(z,Q 2 0) at some low (nonperturbative) input scale Q 2 = Q20 = O(1 GeV ). Therefore one cannot a priori exclude the possibility of non–vanishing polarized parton (f) fragmentation functions into unpolarized hadrons h (= π, K dominantly) ∆D f (z,Q ) ≡ D f+(z,Q )−D f−(z,Q ) (1) in addition to their common unpolarized counterparts D f (z,Q ) ≡ D f+(z,Q ) +D f−(z,Q ) , (2) corresponding to the commonly considered ∆f(x,Q) ≡ f+(x,Q )− f−(x,Q ) (3) f(x,Q) = f+(x,Q ) + f−(x,Q ) . (4) It should be noted that ∆D f (z,Q ) is obviously considered here as a standard leading– twist object of perturbative QCD obeying the common leading–twist Q–evolution equations, factorization properties, etc. The communication between the spectator core and the fragmenting parton was invoked above merely to point out the fact that the nonperturbative boundary condition ∆D f (z,Q 2 0) 6= 0 can not be rejected a priori, but has