Updated Systematics and Methodology

After an overhaul of my asymmetry calculation and systematics I post new money plots. I summarize the changes as the following:

• Extract raw asymmetry, ε, from p₀+p₁×sin(φ_S) fit
• Apply background correction (removal of background asymmetry and scaling for signal fraction) to extracted, raw p₁ from fit
• The statistical uncertainty due to the polarization uncertainty (negligible) has been removed from the calculation to be cited as a ~5% scale systematic (correlated across all bins)
• The statistical uncertainty due to the signal fraction uncertainties (propagated fit parameters and residuals) have been moved from statistical to systematic
• The statistical uncertainty due to the background asymmetry uncertainty (changed to 1.2% for both blue and yellow) has been moved from statistical to systematic
• The systematic uncertainty due to the alternative background asymmetry has been removed
• The systematic uncertainty due to the alternative mass window has been removed

Residuals

I have unsuccessfully attempted to recalculate by hand the content stored in hCountsSysUncertResFit. I summarize my attempt for x_F bin-1 as the following

• Fit a constant to res_1 from 0.1 to 0.2 GeV/c² to obtain 45.97±35.99
• Scale by the number of bins to obtain 919.4±719.8
• Scale by the bin width (0.05) to obtain 45.97±35.99

Figure 1

This does not correspond to the 9.84 found via hCountsSysUncertResFit->GetBinContent(1). It is not clear to me that scaling by the bin width is the right thing to do, but perhaps we can clear that up in the meeting. If I simply take the bin sums I obtain 106.6, which if I scale by the bin width becomes 5.33. For the following figures I simply take the sum across the bins (106.6 in this particular x_F bin).

Calculation

A_N = ( (1/P)×ε-(1-f_sig)×A_{N, bg} )/f_sig

(δA_N)_stat = ( (1/P)×δε )/f_sig

(δA_N)_bg = ( (1-f_sig)/f_sig )×δA_{N, bg}

(δA_N)_{sig. frac. prop} = (A_N-A_{N, bg})×(δf_{sig, prop}/f_sig)

(δA_N)_{sig. frac. res} = (A_N-A_{N, bg})×(δf_{sig, res}/f_sig)

(δA_N)_syst = √( (δA_N)_bg² + (δA_N)_{sig. frac. prop}² + (δA_N)_{sig. frac. res}² )

Money Plots

Figure 2

Figure 3

Table 1: x_F > 0

Table 2: x_F < 0

Mass Window

Our decision to drop the mass-window systematic is justified only if we can demonstrate the differences from our nominal window are dominated by statistics. In Fig. 4 I post the difference between ε extraction from the tight mass window and the high-mass band. The difference is fit with a constant.

Figure 4

xF < 0	xF > 0

In all cases the constant returns a value within 1σ of zero. Additionally, the χ²/ν values are reasonable. One must remember the events are 100% correlated between the x_F binning and the p_T binning. While perhaps not compelling, Figure 4 is suggestive that our mass-window cross-check is statistics-dominated.

Comparison to Published Data

Elke had specifically asked for me to post the average p_T values for the various x_F bins in our comparison plot. I have computed these values for our data, grabbed the published values from the paper, and remade the figure with the latest systematics.

Figure 5

I like this addition in terms of its information. The aesthetics are not quite so pleasing with the E704 data being so low in p_T with the given scale. However, the message is clear. The RHIC data push us to significantly higher p_T. It is too bad we don't have a factor of 10 more statistics in our third bin!