Even though my previous update to the jet group contained a massive amount of information, I was not able to get to everything I had wanted. Here, I post a follow-up addressing some questions raised prior to the meeting as well as questions raised during the meeting.

χ² Distributions

The first issue involves the χ² distributions for the sinusoidal fits. Carl has pointed out that if the scattering is purely statistical, the χ² values should follow the distribution for the specific degrees of freedom. In this case, the Sivers fit has nominally four degrees of freedom, while the Collins(-like) fits have nominally ten.

For the following figures, I separate the data as best I can into independent samples. I fit separately for trigger, x_F > 0 or x_F < 0, η > 0 or η < 0, η_jet bin (Sivers), pion charge state (Collins), and low or high-z (Collins as a function of j_T). I histogram the χ² values separately for x_F > 0 or x_F < 0.

Note: Since I am trying to utilize independent samples, I do not include the "all triggers" fits.

Since I needed one, myself, here's a reminder: the average of the χ² distribution should equal the number of degrees of freedom; the expected distribution is quite asymmetric for low degrees of freedom. I fit the histograms with the distribution as seen in Bevington Appendix C-4 allowing for a floating over-all scale factor. I do not include fits where, due to statistics, there are fewer than the nominal degrees of freedom.

Figure 1

Figure 2

Figure 3

As with the Collins fits as a function of z, the fits as a function of j_T are entirely sensible.

Figure 4

The high-z asymmetries have very few statistics, however, rebinning sufficiently removes the flutuations that one gets a decent picture of the χ². Again, it's completely sane.

Figure 5

The story is much the same for Collins-like.

Figure 6

Figure 7

Finally, the x_F < 0 high-z Collins-like looks nuts, but I suspect it's a result of fewer statistics. Perhaps, it's just an outlier in what appears to be an otherwise perfectly sane statistical cross-check.

The bottom line: This study suggests the statistical uncertainties from the fits provide a realistic estimate of the uncertainties, leaving little room for additional systematic contributions.

Sivers for x_F < 0

Also raised was the issue about Sivers asymmetries for x_F < 0. I have shown these distributions summed over η_jetand trigger but not broken down into η_jet-bins.

Figure 8: Sivers Asymmetry in Bins of η_jet for x_F < 0

All Triggers	JP0	JP1
JP2	AJP	VPDMB

Interestingly, there does appear to be a positive asymmetry for |η| > 0.5 driven by JP2. It appears to be small, but the data points are systematically above the horizontal. This is probably worth some investigation.

Sivers Fits for Individual p_T Bins

The final issue I will address for this update is to look at Sivers fits for individual p_T bins. There appear to be non-zero bins in JP0 and VPDM at high-p_T. One sensible check is to look at the fits themselves for those particular bins. One thought is that these bins may be scarcely populated, leading to unreliable fit information. I also turn my attention to individual fits for x_F < 0, which seem to be systematically above the horizontal.

Figure 9: Sivers Asymmetry Fits for All Triggers, All η, and x_F > 0

6.0 < pT < 7.1 GeV/c
7.1 < pT < 8.4 GeV/c
8.4 < pT < 9.9 GeV/c
9.9 < pT < 11.7 GeV/c
11.7 < pT < 13.8 GeV/c
13.8 < pT < 16.3 GeV/c
16.3 < pT < 19.2 GeV/c
19.2 < pT < 22.7 GeV/c
22.7 < pT < 26.8 GeV/c
26.8 < pT < 31.6 GeV/c
31.6 < pT < 37.3 GeV/c

Figure 10: Sivers Asymmetry Fits for JP1, All η, and x_F > 0

9.9 < pT < 11.7 GeV/c
11.7 < pT < 13.8 GeV/c
13.8 < pT < 16.3 GeV/c
16.3 < pT < 19.2 GeV/c
19.2 < pT < 22.7 GeV/c
22.7 < pT < 26.8 GeV/c
26.8 < pT < 31.6 GeV/c
31.6 < pT < 37.3 GeV/c

Figure 11: Sivers Asymmetry Fits for VPDMB, All η, and x_F > 0

6.0 < pT < 7.1 GeV/c
7.1 < pT < 8.4 GeV/c
8.4 < pT < 9.9 GeV/c
9.9 < pT < 11.7 GeV/c
11.7 < pT < 13.8 GeV/c
13.8 < pT < 16.3 GeV/c
16.3 < pT < 19.2 GeV/c
19.2 < pT < 22.7 GeV/c
22.7 < pT < 26.8 GeV/c
26.8 < pT < 31.6 GeV/c
31.6 < pT < 37.3 GeV/c

Figure 12: Sivers Asymmetry Fits for All Triggers, η < -0.5, and x_F < 0

6.0 < pT < 7.1 GeV/c
7.1 < pT < 8.4 GeV/c
8.4 < pT < 9.9 GeV/c
9.9 < pT < 11.7 GeV/c
11.7 < pT < 13.8 GeV/c
13.8 < pT < 16.3 GeV/c
16.3 < pT < 19.2 GeV/c
19.2 < pT < 22.7 GeV/c
22.7 < pT < 26.8 GeV/c
26.8 < pT < 31.6 GeV/c
31.6 < pT < 37.3 GeV/c

Figure 13: Sivers Asymmetry Fits for JP2, η < -0.5, and x_F < 0

16.3 < pT < 19.2 GeV/c
19.2 < pT < 22.7 GeV/c
22.7 < pT < 26.8 GeV/c
26.8 < pT < 31.6 GeV/c
31.6 < pT < 37.3 GeV/c

Figure 14: Sivers Asymmetry Fits for All Triggers, η > 0.5, and x_F < 0

6.0 < pT < 7.1 GeV/c
7.1 < pT < 8.4 GeV/c
8.4 < pT < 9.9 GeV/c
9.9 < pT < 11.7 GeV/c
11.7 < pT < 13.8 GeV/c
13.8 < pT < 16.3 GeV/c
16.3 < pT < 19.2 GeV/c
19.2 < pT < 22.7 GeV/c
22.7 < pT < 26.8 GeV/c
26.8 < pT < 31.6 GeV/c
31.6 < pT < 37.3 GeV/c

Figure 15: Sivers Asymmetry Fits for JP2, η > 0.5, and x_F < 0

16.3 < pT < 19.2 GeV/c
19.2 < pT < 22.7 GeV/c
22.7 < pT < 26.8 GeV/c
26.8 < pT < 31.6 GeV/c
31.6 < pT < 37.3 GeV/c