Violation of Sum Rules for Twist-3 Parton Distributions

Abstract

Sum rules for twist-3 distributions are reexamined. Integral relations between twist-3 and twist-2 parton distributions suggest the possibility for a $\delta$-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 $O({\alpha }_S)$ on a quark target.

Comments: 11 pages, talk presented at joint workshop on "Physics at a Japanese Hadron Facility (JHF)", Adelaide, Australia, March 14-21, 2002