Light-cone divergence in twist-3 correlation functions

Abstract

It is argued that the definition of the twist-3 transverse momentum dependent correlation functions must be modified if they contain light-like Wilson lines. In the framework of a simple spectator model of the nucleon we show explicitly the presence of a light-cone divergence for a specific twist-3 time-reversal odd parton density. This divergence emerges for all eight twist-3 T-odd correlators and appears also in the case of a quark target in perturbative QCD. The divergence can be removed by using non-light-like Wilson lines. Based on our results we argue that currently there exists no established factorization formula for transverse momentum dependent twist-3 observables in semi-inclusive DIS and related processes.

Figures (1)

• Figure 1: One-loop diagram relevant to the calculation of $g^{\perp}$ for the quark in the scalar diquark model of Ref. brodsky_02a. [h.c.] stands for the Hermitian Conjugate diagram. The thin dashed line depicts the cut of the correlator. In this diagram the diquark (dashed line) interacts through the exchange of a photon with the eikonalized quark (double line).