Next-to-next-to-leading order QCD analysis of the revised CCFR data for xF 3 structure function and the higher twist contributions

We present the results of the next-to-next-to-leading order QCD analysis of the recently revised experimental data of the CCFR collaboration for the xF3 structure function using the Jacobi polynomial expansion method. The effects of the higher twist contributions are included into the fits following the infrared renormalon motivated model. The special attention is paid to the checks of the predictive abilities of the infrared renormalon model and to the independent extractions of the x-dependent shape of the twist-4 contributions to the xF3 structure function in the process of the leading order, next-to-leading order and next-to-next-to-leading order fits of the revised CCFR data. We stress that at the next-to-next-to-leading order the results for αs(MZ) turn out to be almost nonsensitive to the higher-twist terms. We obtain the following result αNNLO s (MZ) = 0.117±0.002(stat)± 0.005(syst)± 0.003(theory). The comparison of the outcomes of our next-to-leading order and next-to-next-to-leading order analysis indicate that the theoretical QCD uncertainties were underestimated in the process of the next-to-leading order determination of αs(MZ), made recently by the CCFR collaboration itself. Presented in part at the QCD session of Recontres des Moriond-97 (March, 1997). 1. The detailed QCD studies of the behavior of the structure functions of the non-polarized deepinelastic scattering (DIS) are still very important both from the phenomenological and theoretical points of view (see e.g. the reviews [1, 2]). The revision [3] of the experimental data of the CCFR collaboration, previously presented in Ref. [4] put on the agenda the reconsideration of the results of the fits of the old CCFR data, performed at the next-to-next-to-leading order (NNLO) of perturbative QCD both without higher twist [5] and with higher twist contributions [6] using the Jacobi polynomial expansion method. The results of application of this method for the extraction of the x-shape of the twist-4 contributions from the NNLO fits of the combined xF3 data (besides the ones analyzed in Ref.[6]) can be found in Ref. [7]. The Jacobi polynomial approach was developed in Refs.[8]-[10] and successfully used in the process of the next-to-leading order (NLO) fits [11]-[14] and NNLO fits [15, 5, 6, 7] of different experimental data. It should be stressed that at the NLO level the results obtained turned out to be in good agreement with the outcomes of applications of the traditional variant of the DGLAP method [16], based on the solution of the integro-differential equation (compare the results of Refs.[13, 5] and Ref.[4] in the case of neutrino-nucleon DIS and of Refs.[11, 12] with the ones of Ref.[17] in the case of the analysis of the data for the F2 structure function, obtained by the BCDMS and SLAC collaborations). However, the Jacobi polynomial expansion method is also giving the possibility to include into the QCD fits the existing information about the NNLO approximations of the coefficient functions and anomalous dimensions of the finite number of Mellin moments of the DIS structure functions, calculated analytically in Refs.[18][20] and Ref. [21] respectively (for the detailed methodological description of the application of the Jacobi polynomial expansion machinery at the NNLO see Ref.[5]). Therefore, in view of the current lack of information about the NNLO corrections to the Alarelli-Parisi kernel, the Jacobi polynomial expansion method turns out to be the unique method of including selfconsistently the available NNLO perturbative QCD effects into the fits of the DIS structure functions data. In the present work we demonstrate once more the compatibility of the DGLAP method and the Jacobi polynomial expansion approach at the NLO level and extract the values of the parameter Λ (4) MS from the revised CCFR data of Ref. [3] (hereafter called as the CCFR’97 data) with taking into account target mass corrections and twist-4 effects, which were introduced in our analysis using the concept of the infrared renormalon (IRR) model of Ref. [22]. At the next stage we include into our analysis the NNLO perturbative QCD corrections. We extract the x-shape of the twist-4 contributions to the xF3 structure function at the leading order (LO), NLO and NNLO and compare it with the IRR model predictions of Ref. [22]. We also get the values of αs(MZ) both at the NLO and NNLO and compare them with the ones obtained by the CCFR collaboration in Ref. [3]. 2. The application of the Jacobi polynomial expansion machinery at the NLO and NNLO was described in detail in Refs.[8]-[10] and Refs.[15, 5] correspondingly. Nevertheless we will introduce again some basic definitions. The NNLO QCD Q2-evolution of the moments of the xF3 structure function MNS n (Q 2) = ∫ 1 0 x F3(x,Q 2)dx (where n = 2, 3, 4, .) is determined by the solution of the renormalization group equation as MNS n (Q 2) MNS n (Q 2 0) = [ αs(Q 2 0) αs(Q) ]γ (0) NS (n)/2β0 Hn(Q 2 0, Q ) , n ≥ 2 (1)