The polarization correction is done fill-by-fill and the total asymmetries are calculated by weighted averages. This affords the chance to evaluate the statistical cross-checks fill-by-fill. The following update looks at distributions to assess the quality of the fits and potential areas for systematic errors.

Figure 1

Figure 1 shows the χ² distribution for all Sivers fits. The resulting distribution is fit with a χ² function where a scale factor and ν are allowed to float. The resulting fits are quite good returning ν values in reasonable agreement with the actual degrees of freedom.

Figure 2

The p₀ values should in principle fluctuate statistically about zero. Figure 2 (top) shows the distributions of all p₀ values as a function of jet p_T for x_F < 0 covering each fill, trigger, and η-bin. The distribution is fit with a constant and the extracted average value is displayed with the χ² and probability. The constant fit quality is quite bad. Figure 2 (bottom) shows the residual distributions assuming a mean of 0. The distributions are fit with gaussians. For x_F > 0 the width is 3σ from 1.

Figure 3: VPDMB

Figure 3 shows the p₀ distribution and residuals for VPDMB triggers. The constant fits appear to be not entirely unreasonable and the residuals are quite consistent with being centered at 0 and σ = 1.

Figure 4: JP0 (0.5 < η < 1)

Figure 4 shows the distributions and residuals for JP0 triggers and 0.5 < η < 1. While the fit for x_F > 0 is quite reasonable, the fit for x_F < 0 is not good at all. This suggests that at least some portion of the features in Fig. 2 are due to JP0 at forward η.

Figure 5: JP1 (-0.5 < η < 0)

Figure 5 shows the distributions and residuals for JP1 triggers with -0.5 < η < 0. The fit for x_F > 0 is quite poor and the width of the residuals is 3σ from 1. Thus, a portion of the features observed in Fig. 2 appears to be from JP1 at mid-rapidity.

Figure 6: JP2

Figure 6 shows the distributions and residuals for JP2 triggers. The fits are of perfectly reasonable quality and the residuals appear to be quite consistent with being centered at zero with width of unity.