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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 bedetermined 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 withconsiderably reduced systematic uncertainties. Based on the new experimentaldata, 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 smallerthan what previous model-based estimates have so far suggested. We discuss theconsequences of this observation for the analysis of deep inelastic scatteringand QCD sum rules studies at finite density for the vector meson and thenucleon, in which this matrix element is being used as an input parameter.

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