Violation of sum rules for twist-3 parton distributions in QCD Original Research Article

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 hL and hL3 (quark–gluon interaction dependent part of hL) explicitly from their moments for a one-loop dressed massive quark. The physics of these results is illustrated by calculating hL(x,Q2) using light-front time-ordered pQCD to O(αS) on a quark target. A δ(x) term is also found in e(x,Q2), but not in gT(x,Q2), to this order in O(αS).