Scheme Dependence in Polarized Deep Inelastic Scattering

We study the effect of scheme dependence upon the NLO QCD analysis of the world data on polarized DIS. The reliability of an analysis at NLO is demonstrated by the consistency of our polarized densities with the NLO transformation rules relating them to each other. We stress the importance of the chiral JET scheme in which all the hard effects are consistently absorbed in the Wilson coefficient functions. PACS numbers:13.60.Hb; 13.88+e; 14.20.Dh; 12.38.-t There has been a major effort in the past decade to obtain reliable information about the polarized parton densities in the nucleon, and especially to try to determine the degree of polarization of the gluon. Aside from its fundamental interest and its potential as a testing ground for QCD, such information is vital for the planning of experiments at the RHIC collider, due to come into operation in 1999. A great improvement in the quality of the data on inclusive deep inelastic scattering of leptons on nucleons has been achieved recently [1, 2, 3] and, concomitantly, several detailed NLO QCD analyses of the data have been carried out [4] [13], of which the most comprehensive are in refs. [7, 13]. It is well known that at NLO and beyond, parton densities become dependent on the renormalization ( or factorization ) scheme employed. It is perhaps less well known that there are significant differences in the polarized case, as a consequence of the axial anomaly and of the ambiguity in the handling of γ5 in n dimensions. In this paper we study the effect of carrying out the data analysis in different schemes, in the MS, AB and what is called the JET scheme, whose importance we wish to stress. In the latter all hard effects are consistently absorbed into the Wilson coefficient functions. The parton densities in each scheme are, by definition, related to each other by certain NLO transformation rules. On the other hand, the Q evolution in each scheme is controlled by the splitting functions (or the anomalous dimensions in Mellin n-moment space) relevant to that scheme. Thus, in principle, for any two schemes labelled 1 and 2 and for any generic polarized density ∆f one has symbolically: NLO data analysis in Scheme 1 ⇒ ∆f1 , (1) NLO data analysis in Scheme 2 ⇒ ∆f2 , (2) NLO transformation rules on ∆f1 ⇒ ∆f2 (3) and it is a major test of the stability of the analysis and of the consistency of the theory that the results for ∆f2 in (2) and (3) should coincide. In fact, built into the theoretical structure is the feature that the two results actually should differ by terms of NNLO order. Hence the degree to which the results agree is a measure of the reliability of carrying out an analysis at NLO. Moreover, in the set of schemes we study, the nonOf course, physical quantities such as the virtual photon-nucleon asymmetry A1(x,Q ) and the polarized structure function g1(x,Q ) are independent of choice of the factorization convention.