ar X iv : h ep - p h / 96 07 22 3 v 1 2 J ul 1 99 6 RAL - TR - 96 - 046 June 1996 THE POLARIZED TWO - LOOP SPLITTING FUNCTIONS
نویسنده
چکیده
We present a brief description of the light-cone gauge calculation of the spin-dependent next-to-leading order splitting functions. It has recently become possible to perform analyses of the spin-dependent parton distributions of a longitudinally polarized hadron at next-to-leading order (NLO) accuracy of QCD. A first such phenomenological NLO study, taking into account all available experimental data on polarized deep-inelastic scattering has been presented in 1 , followed by the analyses 2. An indispensable ingredient here are the polarized two-loop splitting functions (or anomalous dimensions) ∆P (1) ij which appear in the NLO Q 2-evolution equations for the spin-dependent parton densities. Results (in the MS scheme) for the ∆P (1) ij have first been obtained in 3 where the Operator Product Expansion (OPE) formalism was used. The results were afterwards confirmed in 4 using the somewhat more efficient method developed in 5 and employed in the unpolarized case in 6,7,8 , which is based on the factorization properties of mass singularities and on the use of the axial gauge. In this paper we give a brief description of our calculation 4. To begin with, we collect all ingredients for a NLO analysis of longitudinally polarized deep-inelastic scattering in terms of the spin-dependent structure function g 1 (x, Q 2). Beyond LO, there are two different short-distance cross sections, ∆C q and ∆C g , for scattering off incoming polarized quarks and gluons, respectively. Thus the NLO expression for g 1 reads in general:
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