Next - to - next - to - leading order QCD analysis of the CCFR data for xF 3 and F 2 structure functions of the deep - inelastic neutrino - nucleon scattering

The next-to-next-to-leading order (NNLO) non-singlet QCD analysis of the experimental data of the CCFR collaboration of Ref.[1] for the xF3 and F2 structure functions of the deep-inelastic scattering of neutrinos and antineutrinos on the nucleon by means of the Jacobi polynomial expansion method is made. The target mass corrections are also taken into account. We demonstrate that the NNLO corrections have the important effect: they are decreasing the difference between the values of αs(MZ), extracted from the NLO fit of xF3 data and from the NLO non-singlet fit of the combined xF3 and F2 CCFR data. The obtained NNLO results for αs(MZ) are : αs(MZ) = 0.109± 0.003(stat)± 0.005(syst)± 0.003(theor) (from xF3 data) and αs(MZ) = 0.111 ± 0.002(stat) ± 0.003(syst) ± 0.003(theor) (from the combined xF3 and F2 data). We also estimate the values of the order O(α s)-corrections to the Gottfried sum rule. 1. The recent measurements of the CCFR collaboration provide the most precise up to now experimental results for the structure functions (SFs) xF3(x,Q ) and F2(x,Q ) of the deepinelastic scattering (DIS) of neutrinos and antineutrinos on nucleons [1]. The next-to-leading order (NLO) QCD analysis of the available at present data, obtained at Fermilab Tevatron, was made in Ref.[1] with the help of the approach, based on the solution of the corresponding integro-differential equation [2], [3]. The results for the parameter Λ (4) MS were extracted separately from the fits of the observed behavior of the xF3 SF and from the nonsinglet (NS) analysis of the combined available data for xF3 SF at x < 0.5 and for F2 SF at x > 0.5 in the energy regions where the higher-twist corrections were considered as the negligible small effects. In the process of the latter fits the statement was made that the substitution of the data for xF3 by the data for F2 at x > 0.5 is improving the experimental precision of the results obtained due to higher statistics of F2 in this region. The value of the parameter Λ (4) MS , which resulted from the NLO fits of the data for xF3 SF, is [1]: Λ (4) MS = 171± 32(stat)± 54(syst) MeV (1) while the combined NLO NS analysis of xF3 and F2 SFs data gave [1] Λ (4) MS = 210± 28(stat)± 41(syst) MeV . (2) Let us remind that there is also another method of the analysis of DIS data, which is based on the idea of the reconstruction of the SF from its Mellin moments using the expansion of the SF into the series over the Jacobi polynomials [4]. This method was developed in Ref.[5] and Refs.[6, 7] and successfully applied in the process of the NLO fits of DIS data of the BCDMS collaboration [8] and the mentioned above data of the CCFR collaboration [9, 10]. In the last several years the considerable progress was achieved in the area of the analytical evaluation of the characteristics of DIS at the next-to-next-to-leading order (NNLO) of perturbative QCD in the MS-scheme. Indeed, the NNLO corrections were found in Ref.[11] for the coefficient functions of the SF F2, while in Refs.[12, 13] the similar NNLO calculations were made for the SF xF3. The result of Ref.[12] is in agreement with the one for the NLO corrections to the n = 1 moment of xF3, namely to the Gross-Llewellyn Smith sum rule [14], while the results of Ref.[11] are in agreement with the expressions for the NNLO corrections to the coefficient functions of the NS moments of F2 SF, calculated analytically in the case of the even moments with n = 2, 4, 6, 8, 10 [15]. Moreover, in the case of n = 2, 4, 6, 8 the analytical expression of the NNLO corrections to the anomalous dimensions of the NS moments of F2 SF are known at present [16]. Quite recently the analytical result for the NNLO correction to the anomalous dimension of even n = 10 NS moment of F2 SF became available [17]. Together with the expression for the NNLO correction to the QCD β-function [18], which was confirmed in Ref.[19], the results of Refs.[11]-[17] are forming the theoretical background for the extraction of the value of the parameter Λ (4) MS from the NS fits of the DIS data at the level of new theoretical precision, namely with taking into account the effects of the NNLO corrections. We think that it is still rather difficult to push this program ahead in the framework of the integro-differential formalism. Indeed, the analytical dependence of the NNLO corrections to the anomalous dimensions from the number of the related moments n is unknown at present. Moreover, in view of the definite limitations of the possibilities of the distinguished methods of Ref.[20], used in the calculations of Refs.[14]-[17], [19], [21], this information can not be obtained without additional theoretical efforts . This fact does not allow one to calculate at The calculating method, analogous to the ones developed in the first two works of Ref.[20] was also developed for other purposes in Ref.[22]