ar X iv : h ep - p h / 99 10 37 8 v 1 1 8 O ct 1 99 9 QCD analysis of xF 3 at NNLO : the theoretical uncertainties

The next-to-next-to-leading order (NNLO) QCD analysis of the experimental xF3 structure function from CCFR data is performed. The theoretical uncertainties of the analysis are discussed. The study of DIS structure functions has been a fruitful source of information on the structure of the proton and for testing perturbative QCD. Between the most outstanding results of the program of analyzing structure functions in QCD was the early explanation of the scaling violation phenomena. In the last two decades the second order approximation (NLO) has been extensively compared with F2 and xF3 data. More recently the third order terms (NNLO) have been fully calculated for the case of the coefficient functions [1] but only partially for the anomalous dimension part (n = 2, 4, 6, 8 for singlet and non-singlet operators, and n = 10, only in the non-singlet case) [2]. This has allowed the analysis of xF3 [3, 4] and F2 (non singlet [5] and singlet [6]) at NNLO. In this note we review the theoretical uncertainties involved in the analysis of the structure function xF3 at NNLO. For that task, we firstly remind the method of calculation and the most relevant results of the fits. The QCD evolution of the moments is given by: Mn(Q ) Mn(Q0) = ( αs(Q ) αs(Q0) ) γ (0) NS 2β0 AD(n,Q)C(Q) AD(n,Q0)C (Q0) (1) where AD and C come respectively from the anomalous dimensions and coefficient function terms in the renormalization-group equation (see the explicit forms in [4]). The running coupling constant αs(Q ) is obtained from the expression in terms of inverse powers of ln(Q/Λ MS ). Target mass corrections are also added in the calculation of the moments (see [4]). The moments in Eq. (1) at the initial scale are Mn(Q 2 0) = ∫ 1 0 dxxAx(1− x)(1 + γx). The structure function is reconstructed from its moments by using the expansion in terms of orthogonal Jacobi polynomials: