New determination of $\mathcal{S} \mathcal{T} \langle N| \overline{q} D_{\mu} D_{\nu} q |N \rangle$ based on recent experimental constraints

TL;DR

This paper uses recent experimental data on the twist-3 parton distribution function e(x) to more accurately determine a specific nucleon matrix element, revealing it to be significantly smaller than previous estimates and impacting related QCD analyses.

Contribution

It provides a new, experimentally constrained evaluation of the symmetric traceless part of a nucleon matrix element, reducing uncertainties compared to prior model-based estimates.

Findings

The matrix element is at least an order of magnitude smaller than previous estimates.

New experimental data enables more precise determination of the matrix element.

Implications for deep inelastic scattering and QCD sum rule analyses are discussed.

Abstract

The symmetric and traceless part of the matrix element $\mathcal{S} \mathcal{T} \langle N| \overline{q} D_{\mu} D_{\nu} q |N \rangle$ can be determined from the second moment of the twist-3 parton distribution function $e(x)$. Recently, novel experimental data on $e(x)$ have become available, which enables us to evaluate the magnitude of the above matrix element with considerably reduced systematic uncertainties. Based on the new experimental data, we show that $\mathcal{S} \mathcal{T} \langle N| \overline{q} D_{\mu} D_{\nu} q |N \rangle$ is likely to be at least an order of magnitude smaller than what previous model-based estimates have so far suggested. We discuss the consequences of this observation for the analysis of deep inelastic scattering and QCD sum rules studies at finite density for the vector meson and the nucleon, in which this matrix element is being used as an input parameter.