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Violation of Sum Rules for Twist-3 Parton Distributions in QCD

M. Burkardt·Y. Koike
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Abstract

Sum rules for twist-3 distributions are reexamined. Integral relations between twist-3 and twist-2 parton distributions suggest the possibility for a $δ$-function at $x=0$. We confirm and clarify this result by constructing $h_L$ and $h_L^3$ (quark-gluon interaction dependent part of $h_L$) explicitly from their moments for a one-loop dressed massive quark. The physics of these results is illustrated by calculating $h_L(x,Q^2)$ using light-front time-ordered pQCD to ${\cal O}(α_S)$ on a quark target. A $δ(x)$ term is also found in $e(x,Q^2)$, but not in $g_T(x,Q^2)$, to this order in ${\cal O}(α_S)$.

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M. Burkardt, Y. Koike. 2001-11-30. Violation of Sum Rules for Twist-3 Parton Distributions in QCD. https://doi.org/10.1016/s0550-3213(02)00263-8

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