Abstract
Experimental data obtained for the polarized Bjorken sum rule (BSR) Gamma _1^{p-n}(Q^2) are fitted by using predictions derived within a truncated operator product expansion (OPE) approach to QCD. Four QCD versions are considered: perturbative QCD (pQCD) in the {overline{mathrm{MS}}} scheme, Analytic Perturbation Theory (APT), and 2delta and 3delta analytic QCD versions. In contrast to pQCD, these QCD variants do not have Landau singularities at low positive Q^2, which facilitates the fitting procedure significantly. The fitting procedure is applied first to the experimental data of the inelastic part of BSR, and the known elastic contributions are added after the fitting. In general, when 2delta and 3delta QCD coupling is used the fitted curves give the best results, within the Q^2-range of the fit as well as in extended Q^2-intervals. When the fitting procedure is applied to the total BSR, i.e., to the sum of the experimental data and the elastic contribution, the quality of the results deteriorates significantly.
Highlights
Most of the formal aspects of the calculations are relegated to Appendices: in Appendix A we present the form of the leading-twist perturbation coefficients for a general renormalization scale and scheme; in Appendix B we present construction of An, the analogs of perturbative QCD (pQCD) powers an, in extensions of pQCD without Landau singularities; in Appendix C we summarize such extensions [(F)APT, 2δ and 3δ]; in Appendix D we explain how the statistical and systematic uncertainties of the experimental data are reflected in the corresponding uncertainties of the parameters extracted in the fits; and in Appendix E we estimate the effects of the finiteness of the charm quark mass in our evaluations
Where the bar indicates that the expansion is in the MS scheme, and the renormalization scale μ2 is implicitly understood to be equal to the physical scale Q2
The construction of A(Q2) coupling is summarized in Appendix C for various variants of QCD with holomorphic coupling: (F)APT, 2δ and 3δ AQCD, and we refer to that Appendix for more details
Summary
Is an important spacelike QCD observable for various reasons. It is a difference of the first moment of the spin-dependent structure functions of proton and neutron, its isovector nature makes it easier to describe it theoretically, in pQCD in terms of OPE, than the separate integrals of the two nucleons. In this work we fit the theoretical OPE expressions to the experimental BSR results in pQCD, in (F)APT, and two additional extensions of QCD to low Q2, namely the 2δ [32,33] and 3δ [34,35] AQCD The latter two extensions have the coupling A(Q2) [the analog of the pQCD coupling a(Q2)] which is free of Landau singularities and physically motivated in the entire relevant regime of Q2 in the complex plane, Q2 ∈ C\(−∞, −Mt2hr], where Mt2hr 1 GeV2 is a positive threshold scale. Most of the formal aspects of the calculations are relegated to Appendices: in Appendix A we present the form of the leading-twist perturbation coefficients for a general renormalization scale and scheme; in Appendix B we present construction of An, the analogs of pQCD powers an, in extensions of pQCD without Landau singularities; in Appendix C we summarize such extensions [(F)APT, 2δ and 3δ]; in Appendix D we explain how the statistical and systematic uncertainties of the experimental data are reflected in the corresponding uncertainties of the parameters extracted in the fits; and in Appendix E we estimate the effects of the finiteness of the charm quark mass in our evaluations
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
