Polarized Parton Distributions in the Photon and Factorization Scheme Dependence

Spin-dependent parton distributions in the polarized virtual photon are investigated in QCD up to the next-to-leading order (NLO). In the case Λ ≪ P 2 ≪ Q, where −Q (−P ) is the mass squared of the probe (target) photon, parton distributions can be predicted completely up to the NLO, but they are factorization-scheme-dependent. Parton distributions are analyzed in four different factorization schemes and their scheme dependence are discussed. Particular attentions are paid to the axial anomaly effect on the first moments of quark parton distributions, and also to the large-x behaviors of the parton distributions. Gluon distribution in the virtual photon is found to be factorization-scheme independent up to the NLO. YNU-HEPTh-99-102 KUCP-144 November 1999 e-mail address: [email protected] e-mail address: [email protected] In the past few years, the accuracy of the experimental data on the spin dependent structure function g1 of the nucleon has been significantly improved [1]. Using these experimental data together with the already existing world data, it is now possible to extract polarized parton (i.e., quark and gluon) distributions in the nucleon in the framework of perturbative QCD. In fact several groups [2, 3, 4, 5] have carried out the next-to-leading order (NLO) QCD analysis on the polarized parton distributions in the nucleon recently. These parton distributions may be used for predicting the behaviors of other processes such as polarized Drell-Yan reactions and polarized semi-inclusive deep inelastic scatterings, and etc. The first moments of polarized parton distributions are particularly interesting due to their relevance for the spin structure of the nucleon [6, 7], where the axial anomaly plays an important role [8]. However, at the NLO and beyond in perturbative QCD, parton distribution functions become dependent on the factorization (or renormalization) scheme employed. Recently, the first moment of the real photon structure function g 1 has attracted attention in the literature [9, 10, 11]. More recently, the present authors investigated the spin-dependent structure function g 1 (x,Q , P ) of the virtual photon in the NLO in QCD [14]. The advantage in studying the virtual photon target is that, in the case Λ ≪ P 2 ≪ Q, where −Q (−P ) is the mass squared of the probe (target) photon, and Λ is the QCD scale parameter, we can calculate the whole structure function entirely up to the NLO by the perturbative method [15, 16], in contrast to the case of the real photon target where there exist non-perturbative pieces in the NLO. In this paper we analyze the polarized parton distributions in the virtual photon target. The behaviors of the parton distributions can be predicted completely up to the NLO, but, of course, they are factorization-scheme-dependent. We carry out our analysis in four different factorization schemes, (i) MS, (ii) CI (chirally invariant) (it is also called as JET) [17, 18], (iii) AB (Adler-Bardeen) [19], and (iv) OS (off-shell) [19], and see how the parton distributions change in each scheme. In particular, we examine in detail the axial anomaly effect on the first moments and the large-x behaviors of the parton distributions in each scheme. Gluon distribution 1 The NLO QCD analysis on gγ 1 for the real photon target was made by Stratmann and Vogelsang [12]. The leading order QCD correction to gγ 1 was first studied by one of the authors [13].