Non--Singlet QCD Analysis of Deep Inelastic World Data at \boldmath $O(α_s^3)$

TL;DR

This work conducts a comprehensive non-singlet QCD analysis of world charged-lepton DIS data to extract valence quark distributions with correlated uncertainties, using NNLO and N$^3$LO accuracy enabled by three-loop anomalous dimensions and Wilson coefficients. It evolves the valence PDFs in Mellin space, incorporates heavy-flavor, target-mass, and deuteron corrections, and determines the QCD scale and strong coupling constant, finding clear perturbative convergence from NLO to N$^3$LO. The study also quantifies higher-twist contributions at large x and provides moments suitable for lattice comparisons, delivering precise, parameterized valence PDFs and uncertainty estimates. Overall, the results reinforce the stability of $\alpha_s(M_Z^2)$ and $\Lambda_{QCD}^{N_f=4}$ across higher orders and offer a robust non-singlet framework for comparing DIS data with lattice and global analyses.

Abstract

A non--singlet QCD analysis of the structure function $F_2(x,q^2)$ in LO, NLO, NNLO and N$^3$LO is performed based on the world data for charged lepton scattering. We determine the valence quark parton densities and present their parameterization and that of the correlated errors in a wide range of $x$ and $Q^2$. In the analysis we determined the QCD--scale $Λ_{\rm QCD, N_f = 4}^{\bar{\rm MS}} = 265 \pm 27 \MeV {\rm (NLO)}, 226 \pm 25 \MeV {\rm (NNLO)}, 234 \pm 26 \MeV {\rm (N^3LO)}$, with a remainder uncertainty of $\pm 2\MeV$ for the yet unknown 4--loop anomalous dimension, corresponding to $α_s(M_Z^2) = 0.1148 \pm 0.0019 {\rm NLO}, 0.1134 {\tiny{\begin{array}{c} +0.0019 -0.0021 \end{array}}} {\rm NNLO}, 0.1141 {\tiny{\begin{array}{c} +0.0020 -0.0022 \end{array}}} {\rm N^3LO}$. A comparison is performed to other determinations of the QCD scale and $α_s(M_Z^2)$ in deeply inelastic scattering. The higher twist contributions of $F_2^p(x,Q^2)$ and $F_2^d(x,Q^2)$ are extracted in the large $x$ region, subtracting the twist--2 contributions obtained in the NLO, NNLO and N$^3$LO analysis.

Figures (15)

• Figure 1: The MRST parameterization of $(\bar{d} - \bar{u})$MRST02 describing the E866 data E866. Here also compared with a parameterization given in A02.[Courtesy by J. Stirling.]
• Figure 2: Relative size of the NLO contribution due to $c\overline{c}$--production for $m_c = 1.5 \,\hbox{GeV}$ for $F_2^p(x,Q^2)$ in the valence quark region.
• Figure 3: Relative size of the NLO contribution due to $c\overline{c}$--production for $m_c = 1.5 \,\hbox{GeV}$ for $F_2^d(x,Q^2)$ in the valence quark region.
• Figure 4: Relative size of the NLO contribution due to $c\overline{c}$--production for $m_c = 1.5 \,\hbox{GeV}$ for $F_2^{\rm NS}(x,Q^2)= 2 [F_2^p(x,Q^2) - F_2^d(x,Q^2)]$ in the region $0.01 \leq x \leq 0.3$.
• Figure 5: The structure function $F_2^p$ as function of $Q^2$ in intervals of $x$. Shown are the pure QCD fit in NNLO (solid line) and the contributions from target mass corrections TMC (dashed line) and higher twist HT (dashed--dotted line). The arrows indicate the regions with $W^2 > 12.5~{\,\hbox{GeV}^2}$. The shaded areas represent the fully correlated $1\sigma$ statistical error bands.