Non-Singlet QCD Analysis of the Structure Function F_2 in 3-Loops

TL;DR

This work performs a NNLO non-singlet QCD analysis of the structure function F2(x,Q^2) using non-singlet world data to precisely extract valence quark distributions and the strong coupling αs(MZ^2). By employing MVV NNLO anomalous dimensions and 2-loop Wilson coefficients, the authors propagate correlated experimental errors through the QCD evolution in Mellin space, obtaining αs(MZ^2)=0.1135^{+0.0023}_{-0.0026} and fully correlated valence PDFs at Q0^2=4 GeV^2. They report well-determined u_v and d_v distributions with low-order moments, including ⟨u_v−d_v⟩≈0.180±0.005, comparable to lattice results, and provide a robust framework for future lattice and phenomenological comparisons. The results are consistent with other NNLO analyses and the world average, reinforcing the reliability of non-singlet determinations in constraining valence structure and αs.

Abstract

First results of a non--singlet QCD analysis of the structure function $F_2(x,Q^2)$ in 3--loop order based on the non--singlet world data are presented. Correlated errors are determined and their propagation through the evolution equations is performed analytically. The value for $α_s(M_Z)$ is determined to be $0.1135 +/- 0.0023/0.0026$ compatible with results from other QCD analyses. Low moments for $u_v(x)$, $d_v(x)$ and $u_v(x) - d_v(x)$ with correlated errors are calculated which may be compared with results from lattice simulations.

Figures (2)

• Figure 1: The parton density $xu_v$ at the input scale $Q_0^2 = 4.0~{\rm GeV^2}$ (solid line) compared to results obtained by MRST (dashed--dotted line) MRST03 and Alekhin (dashed line) A02. The shaded areas represent the fully correlated $1\sigma$ statistical error bands.
• Figure 2: The parton density $xd_v$ at the input scale $Q_0^2$ with the same conditions as in Figure 1a.