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2006 EEMC Neutral Pions: Updated Systematics
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 p_{0}+p_{1}×sin(φ_{S}) fit
- Apply background correction (removal of background asymmetry and scaling for signal fraction) to extracted, raw p_{1} 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/c^{2} 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})_{bg}^{2} + (δA_{N})_{sig. frac. prop}^{2} + (δA_{N})_{sig. frac. res}^{2} )
Money Plots
Figure 2
Figure 3
Table 1: x_{F} > 0
ε | ε stat error | A_{N} | A_{N} stat err | A_{N} stat err CR | A_{N} stat err Pol | A_{N} total Syst | A_{N} syst err fit-prop | A_{N} syst err fit res | A_{N} syst B.g. A_{N} | A_{N} Mass Win. Cross-check | |
---|---|---|---|---|---|---|---|---|---|---|---|
x_{F} Bin 1 | 0.001786 | 0.006825 | 0.003010 | 0.014597 | 0.014597 | 0.000141 | 0.001963 | -0.000077 | -0.000006 | 0.001961 | -0.000188 |
x_{F} Bin 2 | 0.000509 | 0.006999 | -0.000117 | 0.016238 | 0.016238 | -0.000005 | 0.003163 | -0.000327 | -0.000104 | 0.003145 | -0.006592 |
x_{F} Bin 3 | 0.006957 | 0.016502 | 0.018700 | 0.053226 | 0.053226 | 0.000879 | 0.009739 | 0.003574 | 0.000323 | 0.009054 | -0.028404 |
p_{T} Bin 2 | 0.009429 | 0.012402 | 0.017415 | 0.022950 | 0.022950 | 0.000819 | 0.000618 | 0.000535 | -0.000300 | 0.000080 | 0.009248 |
p_{T} Bin 3 | -0.001749 | 0.008387 | -0.004502 | 0.017844 | 0.017844 | -0.000212 | 0.001996 | -0.000627 | -0.000152 | 0.001889 | -0.008215 |
p_{T} Bin 4 | -0.001423 | 0.009225 | -0.004739 | 0.021716 | 0.021716 | -0.000223 | 0.003465 | -0.000791 | -0.000228 | 0.003366 | -0.001287 |
p_{T} Bin 5 | 0.008464 | 0.012130 | 0.019343 | 0.030253 | 0.030253 | 0.000909 | 0.004539 | 0.001504 | 0.000134 | 0.004281 | -0.010235 |
p_{T} Bin 6 | 0.005614 | 0.017319 | 0.013122 | 0.048455 | 0.048455 | 0.000617 | 0.006444 | 0.001515 | 0.000050 | 0.006263 | -0.003482 |
p_{T} Bin 7 | 0.015997 | 0.025662 | 0.040618 | 0.068806 | 0.068806 | 0.001909 | 0.010842 | 0.009334 | -0.000389 | 0.005502 | -0.011237 |
p_{T} Bin 8 | -0.045464 | 0.030793 | -0.126508 | 0.084057 | 0.084057 | -0.005946 | 0.034284 | -0.033782 | -0.000573 | 0.005819 | -0.041647 |
p_{T} Bin 9 | -0.063955 | 0.058972 | -0.172061 | 0.156623 | 0.156623 | -0.008087 | 0.066870 | -0.066511 | 0.004401 | 0.005337 | -0.062893 |
Table 2: x_{F} < 0
ε | ε stat error | A_{N} | A_{N} stat err | A_{N} stat err CR | A_{N} stat err Pol | A_{N} total Syst | A_{N} syst err fit-prop | A_{N} syst err fit res | A_{N} syst B.g. A_{N} | A_{N} Mass Win. Cross-check | |
---|---|---|---|---|---|---|---|---|---|---|---|
x_{F} Bin 1 | 0.006411 | 0.006824 | 0.013512 | 0.014385 | 0.014385 | 0.000649 | 0.002033 | 0.000536 | 0.000039 | 0.001961 | 0.000621 |
x_{F} Bin 2 | 0.003399 | 0.006999 | 0.007771 | 0.016002 | 0.016002 | 0.000373 | 0.003188 | 0.000500 | 0.000160 | 0.003145 | 0.001433 |
x_{F} Bin 3 | 0.001181 | 0.016486 | 0.003755 | 0.052405 | 0.052405 | 0.000180 | 0.009107 | 0.000976 | 0.000088 | 0.009054 | 0.058065 |
p_{T} Bin 2 | 0.003333 | 0.012402 | 0.006079 | 0.022618 | 0.022618 | 0.000292 | 0.000309 | 0.000261 | -0.000146 | 0.000080 | 0.008343 |
p_{T} Bin 3 | 0.001582 | 0.008385 | 0.003316 | 0.017583 | 0.017583 | 0.000159 | 0.001902 | 0.000220 | 0.000053 | 0.001889 | -0.009815 |
p_{T} Bin 4 | 0.006811 | 0.009224 | 0.015801 | 0.021399 | 0.021399 | 0.000758 | 0.003623 | 0.001289 | 0.000372 | 0.003366 | 0.017972 |
p_{T} Bin 5 | 0.007356 | 0.012136 | 0.018081 | 0.029831 | 0.029831 | 0.000868 | 0.004682 | 0.001890 | 0.000169 | 0.004281 | 0.000734 |
p_{T} Bin 6 | 0.012713 | 0.017292 | 0.035055 | 0.047679 | 0.047679 | 0.001683 | 0.009030 | 0.006502 | 0.000216 | 0.006263 | 0.003563 |
p_{T} Bin 7 | -0.013361 | 0.025672 | -0.035305 | 0.067837 | 0.067837 | -0.001695 | 0.010761 | -0.009240 | 0.000385 | 0.005502 | -0.032221 |
p_{T} Bin 8 | 0.026638 | 0.030765 | 0.071662 | 0.082766 | 0.082766 | 0.003440 | 0.019315 | 0.018415 | 0.000312 | 0.005819 | 0.077817 |
p_{T} Bin 9 | -0.003934 | 0.059059 | -0.010297 | 0.154585 | 0.154585 | -0.000494 | 0.006597 | -0.003869 | 0.000256 | 0.005337 | 0.075118 |
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
x_{F} < 0 | x_{F} > 0 |
---|---|
In all cases the constant returns a value within 1σ of zero. Additionally, the χ^{2}/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!
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