Non-singlet QCD analysis of F_2(x,Q^2) up to NNLO

TL;DR

This paper assesses the practical relevance of NNLO (3-loop) QCD contributions in the flavor non-singlet sector of F2 for electron-proton and electron-deuteron scattering. It develops a detailed NS formalism with Mellin-space evolution, incorporates target-mass corrections, higher-twist parameterizations, and QED effects, and compares MSbar and DIS factorization schemes. The main finding is that NNLO corrections are small (around 1%) in the medium-to-large x region and are eclipsed by scheme choices and nonperturbative higher-twist effects; higher-twist terms significantly improve fit quality. Given current experimental uncertainties on non-singlet F2, these NNLO effects are not observable. The study also highlights the improved perturbative behavior of the DIS scheme and the pivotal role of HT corrections in robust non-singlet QCD analyses.

Abstract

The significance of NNLO (3-loop) QCD contributions to the flavor non-singlet sector of F_2^ep and F_2^ed has been studied as compared to uncertainties (different factorization schemes, higher twist and QED contributions) of standard NLO (and LO) QCD analyses. The latter effects turn out to be comparable in size to the NNLO contributions. Therefore the minute NNLO effects are not observable with presently available data on non-singlet structure functions.

Figures (2)

• Figure 1: Comparison of our NNLO fits with all presently available flavor non--singlet data ref13ref14ref15ref16ref17 used for our analysis. The higher twist (HT) contribution is taken into account according to (13) and (14). The NLO fits are very similar and practically indistinguishable from the ones shown. So is the NNLO HT(10) fit resulting from the cut $Q^2\geq 10$ GeV$^2$. The inset shows our NNLO input valence distributions at $Q^2_0=4\,\mathrm{GeV}^2$. The scales on the left ordinate refer only to $F_2^{p-n}$ where for each fixed value of $x$ we have added the constant in brackets to $F_2^{p-n}$. The scales on the right ordinate refer to $F_2^p$ and to $F_2^d$. The data sets are shown with their normalization factors in parentheses (first entry refers to $F_2^p$, second entry to $F_2^d$) as obtained in the fit. The ZEUS data for $F_2^p$ have been shifted to the right by $5\,\%$ in order to make their error bars distinguishable from the ones of the H1 data.
• Figure 2: The size of perturbative (a) and nonperturbative (b) uncertainties encountered in various perturbative $\alpha_s$--orders of QCD analyses relative to our nominal NLO analysis of $F_{2,\mathrm{NLO}}^{ep}(x,Q^2)$ which always appears in the denominator of the ratios $r$ as defined and discussed in the text. The HT contributions to the fits shown in (b) refer to the cut $Q^2\geq 4$ GeV$^2$, whereas HT(10) refers to a cut $Q^2\geq 10$ GeV$^2$. The typical relative experimental accuracy is illustrated at $x=0.4$ by the vertical bar ($\pm1\,\%$). At larger and smaller values of $x$ the experimental error increases (e.g., the uncertainty is about $\pm2.5\,\%$ at $x=0.55$, and $\pm10\,\%$ at $x=0.18$). All results are shown for $Q^2=40\,\mathrm{GeV}^2$, but the agreement with data at $Q^2=4\,\mathrm{GeV}^2$ and $Q^2=100\,\mathrm{GeV}^2$ is similar.