In their 2011 PRD article, D'Alesio et al. argue that the sin(φ_S+φ_H) and sin(φ_S+2φ_H) Collins(-like) are negligible even under the maximized scenario. To this point, we have taken this assumption at face value. However, it is useful to test this assumption, in particular, under a scenario where we observe non-zero Collins asymmetries. I show the results of the "sum moments" for Collins with p_{T, jet} > 9.9 GeV/c and Collins-like with p_{T, jet} < 9.9 GeV/c.

Figure 1

In Fig. 1 I show the "Collins-sum" moments. At best the asymmetries are greatly suppressed.

Table 1

So, I find a 2.34σ effect for π^- with x_F > 0 and a 2.50σ effect for π⁺ with x_F < 0. The χ² for a constant hypothesis is perfectly reasonable. Given the presence of a non-zero Collins effect and the hot tower issue, it may be that we are sensitive to "leak-through," though, one might expect the p₀'s to suppress this to some measure. Moreover, the Collins effect is only non-zero for x_F > 0.

Figure 2

The Collins-like asymmetry has been shown to be quite small, thus, one would expect minimal leak-through from the Collins-like effect. Again, however, the Collins asymmetry is non-zero; and may also contribute leak-through to the x_F > 0 Collins-like-sum moment.

Table 2

Table 2 summarizes the results of a constant fit to the data shown in Fig. 2. All fits return effects which are quite small. The largest affect is 2.06σ in π^- with x_F < 0. The constant hypothesis is quite reasonable. The worst fit is for π^- with x_F > 0 (2.08σ).