Two-loop calculations for the propagators of gluonic currents. Erratum

This is an erratum to the paper published in Nucl. Phys. B198(1982)508.Comment: 3 pages, Late

The improved 10th order QED expression for a_{\mu} : new results and related estimates

New estimates of the 10th order QED corrections to the muon anomalous magnetic moment are presented. The estimates include the information on definite improved 10th order QED contributions to $a_{\mu}$, calculated by Kinoshita and Nio. The final estimates are in good agreement with the ones, given recently by Kinoshita.Comment: Presented at Working Group 4 of 7th Int. Workshop on Neutrino Factories and Superbeams NuFact05, Frascati 21-26 June 2005; 3 double column pages, LaTe

The NNLO QCD analysis of the CCFR data for xF_3: is there still the room for the twist-4 terms?

The results of the more detailed NNLO QCD analysis of the CCFR data for $xF_3$ SF are presented. The factorization scale uncertainties are analysed. The NNLO results for $alpha_s(M_Z)$ and twist-4 contributions are obtained. Despite the fact that the amplitude of the $x$-shape of the twist-4 factor is consequently decreasing at the NLO and NNLO, our new QCD analysis seems to reveal the remaining twist-4 structure at the NNLO level. The definite N$^3$LO uncertainties are fixed using the [0/2] Pad\'e resummation technique.Comment: LaTeX, 3 pages, 1 figure; to be published in the Proceedings of DIS99 Workshop, Zeuthen, April 19-23; some technical shortcomings are fixed in the file, 2 referencies correcte

Order αs2\alpha_s^2 perturbative QCD corrections to the Gottfried sum rule

The order $\alpha_s^2$ perturbative QCD correction to the Gottfried sum rule is obtained. The result is based on numerical calculation of the order $\alpha_s^2$ contribution to the coefficient function and on the new estimate of the three-loop anomalous dimension term. The correction found is negative and rather small. Therefore it does not affect the necessity to introduce flavour-asymmetry between $\bar{u}$ and $\bar{d}$ antiquarks for the description of NMC result for the Gottfried sum rule.Comment: LaTeX, 7 pages, the discussions of the $\alpha_s^2$ corrections to the anomalous dimension are modified; 1 reference added; to be published in Phys. Lett.

The NNLO non-singlet QCD analysis of parton distributions based on Bernstein polynomials

A non-singlet QCD analysis of the structure function $xF_3$ up to NNLO is performed based on the Bernstein polynomials approach. We use recently calculated NNLO anomalous dimension coefficients for the moments of the $xF_3$ structure function in $\nu N$ scattering. In the fitting procedure, Bernstein polynomial method is used to construct experimental moments from the $xF_3$ data of the CCFR collaboration in the region of $x$ which is inaccessible experimentally. We also consider Bernstein averages to obtain some unknown parameters which exist in the valence quark densities in a wide range of $x$ and $Q^2$. The results of valence quark distributions up to NNLO are in good agreement with the available theoretical models. In the analysis we determined the QCD-scale $\Lambda^ {\bar{MS}}_{QCD, N_{f}=4}=211$ MeV (LO), 259 MeV (NLO) and 230 MeV (NNLO), corresponding to $\alpha_s(M_Z^2)=0.1291$ LO, $\alpha_s(M_Z^2)=0.1150$ NLO and $\alpha_s(M_Z^2)=0.1142$ NNLO. We compare our results for the QCD scale and the $\alpha_s(M_Z^2)$ with those obtained from deep inelastic scattering processes.Comment: 20 pages, 7 figures, published in JHE

The Jacobi Polynomials QCD analysis for the polarized structure function

We present the results of our QCD analysis for polarized quark distribution and structure function $xg_1 (x,Q^2)$. We use very recently experimental data to parameterize our model. New parameterizations are derived for the quark and gluon distributions for the kinematic range $x \epsilon [10^{-8},1]$, $Q^2 \epsilon [1,10^6]$ GeV^2. The analysis is based on the Jacobi polynomials expansion of the polarized structure functions. Our calculations for polarized parton distribution functions based on the Jacobi polynomials method are in good agreement with the other theoretical models. The values of $\Lambda_{QCD}$ and $\alpha_s(M_z)$ are determined.Comment: 23 pages, 8 figures and 4 table

The NLO DGLAP extraction of alpha_s and higher twist terms from CCFR xF_3 and F_2 structure functions data: results and scale dependence

We perform a detailed NLO analysis of the combined CCFR xF_3 and F_2 structure functions data and extract the value of alpha_s, parameters of distributions and higher-twist (HT) terms using a direct solution of the DGLAP equation. The value of alpha_s(M_Z)=0.1222\pm 0.0048 (exp) \pm 0.0026 (theor) is obtained. Our results has a larger central value and errors than the original one of the CCFR collaboration due to model independent parameterization of the HT contributions. The dependence of HT contributions on the QCD renormalization scale is studied.Comment: Contributed to Nucleon99 Proceedings (Frascati, June 7-9, 1999, Italy), to appear in Nucl.Phys.

An Analytical Expression for the Non-Singlet Structure Functions at Small xx in the Double Logarithmic Approximation

A simple analytic expression for the non-singlet structure function $f_{NS}$ is given. The expression is derived from the result of Ref. [1] obtained by low $x$ resummation of the quark ladder diagrams in the double logarithmic approximation of perturbative QCD.Comment: 5 pages, A few comments and refs are adde

Bjorken unpolarized and polarized sum rules: comparative analysis of large-N_F expansions

Analytical all-orders results are presented for the one-renormalon-chain contributions to the Bjorken unpolarized sum rule for the F_1 structure function of nu N deep-inelastic scattering in the large-N_F limit. The feasibility of estimating higher order perturbative QCD corrections, by the process of naive nonabelianization (NNA), is studied, in anticipation of measurement of this sum rule at a Neutrino Factory. A comparison is made with similar estimates obtained for the Bjorken polarized sum rule. Application of the NNA procedure to correlators of quark vector and scalar currents, in the euclidean region, is compared with recent analytical results for the O(alpha_s^4 N_F^2) terms.Comment: 9 page

N^3LO fits to xF_3 data : αs\alpha_s vs 1/Q^2 contributions

The results of approximate N^3LO and detailed NNLO fits to $xF_3$ data of the CCFR'97 collaboration are presented. We demonstrate that $1/Q^2$ non-perturbative corrections to $xF_3$ modeled by three independent procedures are shadowed by perturbative QCD effects, starting at the NNLO. Special attention is paid to revealing the role of the recently calculated NNLO corrections to the anomalous dimensions and $N^3$LO corrections to the coefficient functions of odd moments of $xF_3$ with $n\leq 13$. The related values of $\alpha_s(M_Z)$ are extracted.Comment: 5 pages, 1 figure, LaTeX; Contributed to the Proceedings of joint 6th Symposium RADCOR 2002 and 6th Zeuthen Workshop Loops and Legs in Quantum Field Theory, September 8-13, Kloster Banz, Germany; size of postscript figure fixe