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Fixation of theoretical ambiguities in the improved fits to $xF_3$ CCFR data at the next-to-next-to-leading order and beyond

A. L. Kataev, G. Parente, A. V. Sidorov

TL;DR

The paper refines the QCD analysis of CCFR'97 xF3 data by incorporating NNLO anomalous dimensions and N^3LO coefficient functions, and by systematically exploring twist-4 power corrections using infrared renormalon and alternative models. It demonstrates a strong interplay between higher-order perturbative QCD effects and 1/Q^2 corrections, achieving stable extractions of $\alpha_s(M_Z)$ close to the world average and showing reduced scale dependence at NNLO and beyond. The study also extends the analysis to up to $n\le 13$ Mellin moments via improved interpolation and Padé techniques, and verifies the robustness of high-twist duality across models. Overall, it provides a more precise, theory-driven framework for DIS neutrino-nucleon structure functions and highlights the residual theoretical uncertainties from thresholds and scales.

Abstract

Using the results for the NNLO QCD corrections to anomalous dimensions of odd $xF_3$ Mellin moments and N$^3$LO corrections to their coefficient functions we improve our previous analysis of the CCFR'97 data for $xF_3$. The possibility of extracting from the fits of $1/Q^2$-corrections is analysed using three independent models,including infrared renormalon one. Theoretical quetion of applicability of the renormalon-type inspired large-$β_0$ approximation for estimating corrections to the coefficient functions of odd $xF_3$ and even non-singlet $F_2$ moments are considered. The comparison with [1/1] Padé estimates is given. The obtained NLO and NNLO values of $α_s(M_Z)$ are supporting the results of our less definite previous analysis and are in agreement with the world average value $α_s(M_Z)\approx 0.118$. We also present first N$^3$LO extraction of $α_s(M_Z)$. The interplay between higher-order perturbative QCD corrections and $1/Q^2$-terms is demonstrated. The results of our studies are compared with those obtained recently using the NNLO model of the kernel of DGLAP equation and with the results of the NNLO fits to CCFR'97 $xF_3$ data, performed by the Bernstein polynomial technique.

Fixation of theoretical ambiguities in the improved fits to $xF_3$ CCFR data at the next-to-next-to-leading order and beyond

TL;DR

The paper refines the QCD analysis of CCFR'97 xF3 data by incorporating NNLO anomalous dimensions and N^3LO coefficient functions, and by systematically exploring twist-4 power corrections using infrared renormalon and alternative models. It demonstrates a strong interplay between higher-order perturbative QCD effects and 1/Q^2 corrections, achieving stable extractions of close to the world average and showing reduced scale dependence at NNLO and beyond. The study also extends the analysis to up to Mellin moments via improved interpolation and Padé techniques, and verifies the robustness of high-twist duality across models. Overall, it provides a more precise, theory-driven framework for DIS neutrino-nucleon structure functions and highlights the residual theoretical uncertainties from thresholds and scales.

Abstract

Using the results for the NNLO QCD corrections to anomalous dimensions of odd Mellin moments and NLO corrections to their coefficient functions we improve our previous analysis of the CCFR'97 data for . The possibility of extracting from the fits of -corrections is analysed using three independent models,including infrared renormalon one. Theoretical quetion of applicability of the renormalon-type inspired large- approximation for estimating corrections to the coefficient functions of odd and even non-singlet moments are considered. The comparison with [1/1] Padé estimates is given. The obtained NLO and NNLO values of are supporting the results of our less definite previous analysis and are in agreement with the world average value . We also present first NLO extraction of . The interplay between higher-order perturbative QCD corrections and -terms is demonstrated. The results of our studies are compared with those obtained recently using the NNLO model of the kernel of DGLAP equation and with the results of the NNLO fits to CCFR'97 data, performed by the Bernstein polynomial technique.

Paper Structure

This paper contains 15 sections, 52 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Anomalous dimensions and coefficient functions: approximate vs exact results
  4. Results of the fits without twist-4 terms
  5. Incorporation of the twist-4 terms
  6. Infared renormalon model parameterization
  7. IRR approach and naive non-Abelianization
  8. The determination of $\alpha_s(M_Z)$ values and their scale-dependence uncertainties
  9. Determination of the $x$-shape of the twist-4 corrections
  10. Comparison with the results of other NNLO analyses
  11. Comments on estimates of scale-scheme dependence uncertainties.
  12. Comments on outputs of the NNLO Bernstein polynomial analyses
  13. The model independence of high-twist duality effect
  14. Conclusions
  15. Acknowledgements

Figures (1)

  • Figure 1: The $x$-shapes of $h(x)$ extracted from the fits to $xF_3$ CCFR'97 data in different orders of perturbative theory. The initial scale is chosen at $Q_0^2=20~GeV^2$. The cases of different $N_{max}$ are considered. a) $N_{max}$=6; b) $N_{max}$=7; c) $N_{max}$= 8; d) $N_{max}$=9