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

Non-perturbative momentum dependence of the coupling constant and hadronic models

Models of hadron structure are associated with a hadronic scale which allows by perturbative evolution to calculate observables in the deep inelastic region. The resolution of Dyson-Schwinger equations leads to the freezing of the QCD running coupling (effective charge) in the infrared, which is best understood as a dynamical generation of a gluon mass function, giving rise to a momentum dependence which is free from infrared divergences. We use this new development to understand why perturbative treatments are working reasonably well despite the smallness of the hadronic scale.Comment: Changes in Acknowledgments and PACS number

The role of different schemes in the QCD analysis and determination of the strong coupling

In this article, we present a Next-to-Leading Order (NLO) QCD analysis to study the role and influence of different schemes on simultaneous determination of the Parton Distribution Functions (PDFs) and strong coupling, αs(MZ2). We perform our analysis based on three different data sets, HERA I and II combined data, H1-ZEUS charm combined data, and H1 and ZEUS beauty production cross sections data, in two different Thorne–Roberts (TR or RT) and Thorne–Roberts Optimal (RT OPT) schemes. We show in going from RT scheme to RT OPT scheme, in addition of reduction the uncertainty of some PDFs, specially for the gluon distribution, we get ∼0.4% and ∼0.7% improvement in the fit quality and ∼0.9% and ∼1.6% improvement for the strong coupling, αs(MZ2), without and with heavy flavor contributions, respectively