Following up on a previous update, I now show the sate of the Collins-like 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

It is worth examining the angular coverage of φ_S vs. φ_S-2φ_h. One can see the coverage is rather similar to what one sees for the Collins 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⁺)

One immediately notices the number of points below the horizontal for positive x_F. The constant fit for η > 0 is consistent with zero, however both the "All η" and "η < 0" panels show small negative effects (2.65σ and 3.29σ, respectively). For negative x_F, the constant fit is not quite what one would hope (χ²/ν = 1.4), but the fits are within 1σ of zero.

One issue worth pointing out is that the plots hint at a negative effect, while the D'Alesio, Murgia, and Pisano paper shows a positive effect. Theirs was a maximized prediction, and there is always the possibility for sign ambiguities. Thus, one should be rather cautious before jumping to conclusions at this very early stage.

Figure 3: Asymmetry (π^-)

Interestingly, the constant fits for π^- all return values well within 1σ of zero. So, again, one should proceed with caution in drawing conclusions this early.

Figure 4: p₀ from Fit (π⁺)

One finds perfectly reasonable distributions for positive x_F. However, for negative x_F, there appears to be a fair amount of structure in both hemispheres.

Figure 5: p₀ from Fit (π^-)

The story with π^- is similar to that of Fig. 4. This time, however, the behavior of η < 0 is much better than η > 0. This could suggest a cut to limit the range of forward rapidity is appropriate.

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⁺)

The negative trend is reflected across the various trigger combinations. In particular, the constant fits return greater than 1σ effects for JP2 (2.31σ) and VPDMB (2.61σ).

Figure 7: Asymmetry (π^-)

It is difficult to discern a consistent trend in π^-. A few bins are suggestive of a positive trend at low-z, however, it is by no means conclusive.

Figure 8: p₀ (π⁺)

JP0, JP1, and AJP show offsets greater than 1σ. Additionally, the fit quality is not quite what one might hope. Integrated over the triggers, of course, the fit is perfectly fine.

Figure 9: p₀ (π^-)

The fits for π^- are a bit more well behaved.

x_F < 0

Figure 10: Asymmetry (π⁺)

There appears to be quite a bit of fluctuation between the various trigger combinations. JP0, JP2, AJP, and VPDMB all show offsets greater than 1σ from zero. Also, the fits are often not of good quality.

Figure 11: Asymmetry (π^-)

Once again, the π^- distributions are more well behaved than π⁺. Only VPDMB turns out an offset greater than 1σ from zero (1.18σ).

Figure 12: p₀ (π⁺)

There seems to be quite a bit of structure to these distributions. While the offsets are typically less than 1σ from zero, the fit quality is not very good.

Figure 13: p₀ (π^-)

Again, there is some fluctuation and structure in these distributions.

Further Statistical Cross-checks

Figure 14: χ²-Distribution for Collins-like Fits

Figure 14 shows the χ² distribution for the Collins-like fits (p₀+p₁×sin(φ_S-2φ_h)). In red is plotted the expected distribution for ν = 10. The agreement with expectation is quite good.

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. With only four points, the negative x_F fit is too good. The fit in positive x_F is not good at all.

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, but the distribution is quite nice. The fits appear quite 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.

Figure 17: Asymmetry Fits

Again, the asymmetry fits do not return a good distribution. The fitter finds a Gaussian for negative x_F, but the uncertainties on the mean and width are enormous.

Figure 18: p₀ Fits

The distribution of fits to p₀'s is somewhat better than the asymmetries, though positive x_F is still fairly scattered. The uncertainties are quite large, but the fitted means are consistent with zero.

η Dependence

π⁺

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.

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