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extra gluon. As in Ref. [17], we focus on the calculation of an SSA. We start with graphs of the type shown in Fig. 3, where the extra gluon attaches on the side of the hard part nearest to its parent hadron. Any spin asym- metry disappears in the zeroth order cross section, Fig. 1 because there are too few Dirac matrices to produce a non-zero result in the traces with γ$_{5}$ . 

Consider, for example, Fig. 3(a). The arrow on the gluon line indicates that it is collinear to H$_{1}$ . By first deforming the l integral out of the Glauber region to the H$_{1}$ -collinear region, one may replace the intermediate struck quark line of momentum k$_{3}$ − l by the eikonal factor 

<img src='content_image/439269.jpg'>

where n µ 1 ≡ (0 , 1 , 0$_{t}$ ). The sign on the iϵ is determined by the direction of the contour deformation. For the spin- dependent part, the attachment of the extra gluon at the spectator produces a factor at leading power equal to 

<img src='content_image/439270.jpg'>

When this expression is combined with the imaginary part of Eq. (8), the factors of − i and i combine and a contribution to an SSA is obtained. The ϵ$_{jk}$ is the two- dimensional Levi-Civita symbol with ϵ$_{12}$ = 1. 

If the extra gluon is on the other side of the cut as in Fig. 3(b), the eikonal factor is 

<img src='content_image/439267.jpg'>

The factor from the attachment at the spectator is, 

<img src='content_image/439268.jpg'>

When this is combined with the imaginary part of Eq. (10), the factors of i and − i combine and a contribu- tion to an SSA is again obtained. It is exactly equal to the one found in Fig. 3(a) as it must be since the graphs are related by Hermitian conjugation. 

Analogous steps apply to Figs. 3(c,d). The different shadings on the arrows is to emphasize that they are ra- diated from H$_{2}$ rather than H$_{1}$ . Now, after a contour 

