Scale dependence of twist-three contributions to single spin asymmetries

We reexamine the scale dependence of twist-three correlation functions relevant for the single transverse spin asymmetry in the framework of collinear factorization. Evolution equations are derived for both the flavor-nonsinglet and flavor-singlet distributions and arbitrary parton momenta. Our results do not agree with the recent calculations of the evolution in the limit of vanishing gluon momentum. Possible sources for this discrepancy are identified.

Figure 1

Support properties of the parton correlation functions (4) in the $(x,x_2)$ plane.

Figure 2

Support properties of the correlation functions (5) in barycentric coordinates. For the explanation of different regions and lines see text.

Figure 3

Integration regions in Eq. (43).

Figure 4

The exchange diagram.