Spin-Dependent Parton Distributions of the Longitudinally Polarized Photon Beyond the Leading Order

A next-to-leading order (NLO) QCD analysis of the spin-dependent parton distributions ∆f(x,Q) of the longitudinally polarized photon and of its structure function g 1 (x,Q ) is performed within the framework of the radiative parton model. The important issues of a suitably chosen factorization scheme and related boundary conditions are discussed in detail. The typical effects of the NLO corrections are quantitatively studied for two very different conceivable scenarios for the NLO polarized parton distributions ∆f(x,Q). More accurate measurements of the nucleon’s spin asymmetry A1 (x,Q ) ≃ g 1 (x,Q )/ F 1 (x,Q ) in polarized deep-inelastic scattering (DIS) [1], covering also a wider range in (x,Q) and providing results for different targets (N = n, d) as compared to early measurements of Ap1(x,Q ) [2], have considerably improved our knowledge about the nucleon’s spin structure in the past few years and also renewed the theoretical interest in this field. This is also due to the possibility to perform now a complete and consistent QCD analysis of polarized DIS in NLO, since the required spin-dependent two-loop splitting functions ∆P (1) ij have been calculated recently [3, 4]. A first such NLO analysis in the MS scheme has been presented in [5] based on the phenomenologically successful concept of the radiative parton model, i.e., the generation of parton distributions from a valence-like structure at some low-resolution scale μ, which had previously led, e.g., to the prediction [6] of the small-x rise of the unpolarized proton structure function F p 2 (x,Q ) as observed at HERA [7]. Subsequent NLO studies [8] have imposed different boundary conditions and/or factorization schemes. The knowledge of the two-loop splitting functions ∆P (1) ij [3, 4] also offers the opportunity to perform a similar NLO QCD analysis of the spin-dependent parton content ∆f of the longitudinally (more precisely, circularly) polarized photon because the required twoloop photon-to-parton splitting functions ∆k q ≡ ∆P (1) qγ and ∆k (1) g ≡ ∆P (1) gγ can be easily obtained from ∆P (1) qg and ∆P (1) gg , respectively. Although such a study seems to be somewhat premature in view of the lack of any experimental information on ∆f up to now, interesting theoretical questions arise when going beyond the leading order. Apart from getting a feeling for the typical size of the NLO corrections it is moreover important to analyse the necessity (and feasibility) to introduce a suitable factorization scheme which overcomes expected problems with perturbative instabilities arising in the MS scheme in particular for large values of x. Such instabilities were found in the unpolarized case where they were eliminated [9] by absorbing the the ’direct-photon’ contribution to F γ 2 into the NLO photonic quark distributions (DISγ scheme). In this paper we will show that a similar procedure is also recommendable in the polarized case, where it works equally well.