Money Plots

Following the March 28 spin call, we decided to proceed with the following changes:

• Drop the 4-5 GeV/c p_T-bin
• Drop the 12-16 GeV/c p_T-bin
• Adopt the previously described systematics proposal, e.g. drop the mass window from the systematics and replace with the uncertainties due to Pythia functional form fits.

Implementing the changes required rerunning the analysis code for data and Monte Carlo to apply the new p_T acceptance for binning in x_F. An additional change is to include the non-collision background systematic in the calculation. Systematics are now small enough as to make our non-collision estimate relevant. While our upper-limit is, likely, a gross over-estimate, systematics are still well below our statistical uncertainties even with its inclusion. For practical purposes, we do not gain anything by spending time to fine tune our non-collision systematic. Given a factor of 10 more data, revisiting the non-collision systematic may be appropriate. In this post I show the updated money plots, data tables, and supporting figures. Note: plots labeled "STAR Preliminary" have not yet been released. The labels are there for the purpose of fine-tuning cosmetics.

Figure 1: Asymmetries

Figure 1 shows the updated asymmetry plot for x_F and p_T bins. Note, again, this plot has not been released; "STAR Preliminary" is posted as we fine-tune cosmetics. As discussed during the spin call, I have implemented some comsmetic changes:

• labels for the reaction: p^↑ + p → π⁰ + X
• center-of-mass energy: √s = 200 GeV
• pseudorapidity range: 0.8 < η_π⁰ < 2

The p_T range has been restricted and also enforced for x_F. The highest-x_F point has moved, perhaps, more than one might expect. However, this bin is quite low on statistics; and we have already observed interesting phenomena which appear to be statistics-related.

Figure 2: Constant of Fit

Figure 2 shows the extracted raw-asymmetry fit constants. This figure is not intended for public consumption, but it is a nice internal cross-check of Fig. 1. As Table 3 shows, constant fits to the p₀'s for x_F > 0 are 2σ from zero. The χ² for the x_F fit for x_F < 0 is 2σ from expectation.

Figure 3: Comparison to Published Data

Again, Fig. 3 has been updated with the same cosmetics as described for Fig. 1. I have also included the average pseudorapidity for the FPD data. Renee had mentioned wanting to discuss the cosmetics of the E704 bin widths. I also considered including the average pseudorapidity of the E704 data. I have estimated this to be ~2.5, but I have not found confirmation of this.

Mass Window Cross-checks

Much work has gone into ruling out the mass-window as a valid systematic. It may be excluded if it can be demonstrated that fluctuations due to the mass window are from statistics.

Figure 4: Mass Window Comparisons

Shown in Fig. 4 are the raw asymmetries for three different mass windows. The red and gray points should be totally uncorrelated, while the black points contain all of the events in red and gray. By eye the scattering appears to be statistical for x_F < 0. This is not so clear for x_F > 0.

Figure 5: Difference of Raw Asymmetries

In Fig. 5 is plotted the difference in the raw asymmetries for the tight window (0.105 < m_γγ < 0.165 GeV/c²) and that of the high-mass band (0.165 < m_γγ < 0.2 GeV/c²). The events in these sample are completely uncorrelated. Indeed, it is difficult to argue that for x_F < 0, the scattering is not statistical. The difference in cross ratios is within 1σ of zero, and the fits return perfectly reasonable χ²'s. The case is a bit trickier for x_F > 0. The offset is perfectly reasonable (1.1σ), however the χ² values are very small. For p_T-binning, the value is not too unlikely (Prob. = 0.953), however, the value for x_F binning is quite unlikely (0.997). On the other hand, for the null hypothesis χ²/ν = 1.234/3 which is perfectly reasonable (Prob. = 0.745). For completeness sake, the null hypothesis yields χ²/ν = 2.255/6 (Prob. = 0.895) for the p_T binning.

Formulae

Here, I post the relevant formulae used in the calculations.

Data Tables

Table 1: x_F > 0

Note: the non-collision background systematic (over-estimate) is now included. It is not wholly irrelevant, however, in only one case it leads. Below the bins for high-kinematics, the background asymmetry systematic leads. For the high-kinematic bins, the systematic from propagation of the Pythia functional form fit uncertainties leads. Also, note that the polarization systematic is also not included in the calculation. It is cited on the figure as a 4% relative scale uncertainty.

Table 2: x_F < 0

The story is much the same for Table-2.

Table 3: Constant Fits to Extracted p₀'s

The p₀ for positive x_F is 2σ. The χ² for negative-x_F (x_F binning) is 2.1σ. The χ² for negative-x_F (p_T-binning) is 1.37σ.

Table 4: Constant Fits to A_N

Note: the bins are somewhat correlated through the polarization and background correction. The negative x_F asymmetry is a 1σ effect.

Raw Asymmetry Extraction

Below I post the figures showing the extraction of the raw asymmetries. I show plots for both x_F > 0 and x_F < 0.

Figure 6: x_F Bins

xF > 0	xF < 0
0.06 < xF < 0.13
0.13 < xF < 0.20
0.20 < xF < 0.27

Figure 7: p_T Bins

xF > 0	xF < 0
5 < pT < 6 GeV/c
6 < pT < 7 GeV/c
7 < pT < 8 GeV/c
8 < pT < 9 GeV/c
9 < pT < 10 GeV/c
10 < pT < 12 GeV/c

Single-arm Measurement

One useful check is to examine the raw asymmetries as extracted with the traditional single-arm measurement. Using the same function form for the fit, the p₁'s should be consistent and the single-arm p₀ should reflect the luminosity asymmetry.

Figure 8: x_F Bins

xF > 0	xF < 0

Figure 9: p_T Bins

xF > 0	xF < 0