Perturbative generation of a strange-quark asymmetry in the nucleon

TL;DR

The paper shows that NNLO perturbative QCD evolution, driven by the three-loop splitting function $P_{ns}^{(2)S}$, generates a nonzero strange–antistrange asymmetry $s(x)-\bar{s}(x)$ in the nucleon even when the input at the initial scale is symmetric. This arises because the nucleon’s nonzero valence up and down densities cause a difference between quark-to-quark and quark-to-antiquark splittings at NNLO. The authors derive the non-singlet evolution framework, provide a moment-space solution for the generated asymmetry, and present numerical estimates indicating a small but finite asymmetry with a negative second moment around $-5\times10^{-4}$ at $Q^2=20$ GeV$^2$. They discuss the implications for interpretations of the NuTeV anomaly and compare with global PDF analyses, highlighting that perturbative generation of $s-\bar{s}$ is a robust prediction of QCD at NNLO.

Abstract

We point out that perturbative evolution in QCD at three loops generates a strange-antistrange asymmetry s(x)-sbar(x) in the nucleon's sea just from the fact that the nucleon has non-vanishing up and down quark valence densities. The recently computed three-loop splitting functions allow for an estimate of this effect. We find that a fairly sizable asymmetry may be generated. Results for analogous asymmetries in the heavy-quark sector are also presented.

Figures (2)

• Figure 1: Example of (a) virtual and (b) real diagrams contributing to $P_{ns}^{(2) S}$
• Figure :