Higher twists and $\alpha_s(M_Z)$ extractions from the NNLO QCD analysis of the CCFR data for $xF_3$ structure function

TL;DR

This paper performs a detailed NNLO QCD analysis of CCFR data for the $xF_3$ structure function, estimating theoretical uncertainties and extracting $oldsymbol{ ext{alpha}_s(M_Z)}$ with twist-4 contributions considered.

Contribution

It introduces a comprehensive NNLO analysis including twist-4 terms, estimates theoretical uncertainties with Padé resummation, and provides refined $oldsymbol{ ext{alpha}_s(M_Z)}$ values from CCFR data.

Findings

NNLO analysis yields $ ext{alpha}_s(M_Z)=0.118 ext{ to } 0.121$ with uncertainties.

Twist-4 contributions decrease at NNLO but may still be present.

Theoretical uncertainties are estimated using Padé resummation and scale variation.

Abstract

A detailed next-to-next-to-leading order (NNLO) QCD analysis is performed for the experimental data of the CCFR collaboration for the $xF_3$ structure function. Theoretical ambiguities of the results of our NNLO fits are estimated by application of the Pad\'e resummation technique and variation of the factorization and renormalization scales. The NNLO and N$^3$LO $\alpha_s(Q^2)$ $\bar{MS}$-matching conditions are used. In the process of the fits we are taking into account of twist-4 $1/Q^2$-terms. We found that the amplitude of the $x$-shape of the twist-4 factor is decreasing in NLO and NNLO, though some remaining twist-4 structure seems to retain in NNLO in the case when statistical uncertainties are taken into account. The question of the stability of these results to the application of the [0/2] Pad\'e resummation technique is considered. Our NNLO results for $\alpha_s(M_Z)$ values, extracted from the CCFR $xF_3$ data, are $\alpha_s(M_Z)=0.118 \pm 0.002 (stat) \pm 0.005 (syst)\pm 0.003 (theory)$ provided the twist-4 contributions are fixed through the infrared renormalon model and $\alpha_s(M_Z)=0.121^{+0.007}_{0.010}(stat)\pm 0.005 (syst) \pm 0.003 (theory)$ provided the twist-4 terms are considered as free parameters.