Following up on previous updates, I now show the sate of the Collins vs. j_T analysis after integrating the full statistics. As before, this should in no way be considered final. Very few cuts have been implemented at this point, and hopefully this analysis will motivate a sensible set.

As before, each plot is fit with a constant. For negative x_F and for p₀ distributions, this is a sensible expectation. One may hope to see a signal for positive x_F, and comparing to a constant may illuminate such a variation.

NOTE: Asymmetries are not corrected for polarization and error bars are statistical only.

Figure 1: Angular Coverage

As a reminder, I show the angular coverage of φ_S vs. φ_S-φ_h. One can see the coverage is rather similar to what one sees for the Collins-like angle.

Hemisphere Dependence

One useful check is to examine the asymmetries in the two hemispheres. All things being equal, the answers should be the same. However, I have not implemented a fiducial volume cut (e.g. |η| < 1), so the acceptance is different for the two hemispheres. Likely, I will need to implement such a cut in the near future.

Figure 2: Asymmetry (π⁺)

None of the fits are particularly good. While we don't necessarily expect constant behavior for positive x_F, the fits for negative x_F are espeically troubling.

Figure 3: Asymmetry (π^-)

The fits for Fig. 3 are significantly better than those for Fig. 2. No signal appears to be present, however, that may not be entirely suprising.

Figure 4: p₀ from Fit (π⁺)

Again, the fits for negative x_F are troubling. In this case, it appears the culprit is the negative hemisphere. The positive hemisphere shows a bit of an offset from zero (1.74σ).

Figure 5: p₀ from Fit (π^-)

The individual fits for positive x_F seem fine, however, the combined fit is a bit worse than one would hope. On the other hand, the combined fit for negative x_F is decent, while the fit for the negative hemisphere is quite bad.

Trigger Dependence

It is also useful to examine the calculations for the different triggers. One may expect consistent answers in overlap regions. Wide variations may signal systematic effects.

x_F > 0

Figure 6: Asymmetry (π⁺)

It is difficult to discern a signal trend from these data.

Figure 7: Asymmetry (π^-)

Again, discerning a signal is difficult. Perhaps, one might imagine a bit of a bias toward negative values, but by no means would I say anything conclusive at this stage.

Figure 8: p₀ (π⁺)

Aside from AJP, the fits are not terrible. There is a bit of an offset in VPDMB but not a large effect (1.79σ).

Figure 9: p₀ (π^-)

Here, the fit quality seems limited by JP1.

x_F < 0

Figure 10: Asymmetry (π⁺)

Obviously, something is amiss with VPDMB. Overall, the fit quality is not good.

Figure 11: Asymmetry (π^-)

The fits for Fig. 11 are not bad. AJP shows a 1.54σ offset.

Figure 12: p₀ (π⁺)

Again, something is not right with VPDMB. The fits for JP2 and AJP are not great.

Figure 13: p₀ (π^-)

The fit for VPDMB is not great. There is also a 2σ offset in AJP.

Further Statistical Cross-checks

Figure 14: χ²-Distribution for Collins-like Fits

Figure 14 shows the χ² distribution for the Collins fits (p₀+p₁×sin(φ_S-φ_h)). In red is plotted the expected distribution. On top, the distribution is forced to have ν = 10; and the agreement with expectation is quite good. On bottom, the fit allows ν to float. The fits are of fine quality, and ν is found to be close to the expected value (< 1σ for positive x_F and 1.86σ for negative x_F).

Distribution of Constant Fits

Figure 15: Asymmetry Fits

In Fig. 15 I show the distribution of constant fits to the asymmetries weighting the entries by 1/uncertainty. There simply are not many fits, thus, it is difficult to glean much information. The distributions are fit with a Gaussian. Thes fits show means consistent with zero and similar widths.

Figure 16: p₀ Fits

In Fig. 16, I show the weighted distribution for fits to the p₀'s. Again, there are not many fits from which to draw. The fits appear decently Gaussian with means consistent with zero and similar widths.

Reduced χ² of Constant Fits

With such a low number of fits with varying degrees of freedom, it is impossible to perform a χ² study of the constant fits. However, we can examine the reduced χ²'s for some information. The distribution for the asymmetries was simply too scattered for this study, so it has been excluded.

Figure 17: p₀ Fits

The distribution for negative x_F is not very informative. The uncertainties in positive x_F are large, but the fitted mean is consistent with zero.

Figure 18: p₀ Fits

The distribution of fits to p₀'s is somewhat better than the asymmetries. The uncertainties are large, but the fitted means are consistent with zero and the widths are consistent.

η Dependence

The distributions in Fig. 15- Fig. 18 are taken from fits to the various triggers in different hemispheres. In Fig. 19-Fig. 28 I show the results of these fits.

π⁺

Figure 19: JP0 Triggers

Figure 20: JP1 Triggers

Figure 21: JP2 Triggers

Figure 22: AJP Triggers

Figure 23: VPDMB Triggers

π^-

Figure 24: JP0 Triggers

Figure 25: JP1 Triggers

Figure 26: JP2 Triggers

Figure 27: AJP Triggers

Figure 28: VPDMB Triggers