Review of the systematic uncertainties for the cross section and longitudinal spin asymmetries.

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Spin Asymmetries

The sizable systematic uncertainties included in the final results include:

1. The "propagated" uncertainty on the signal fraction, which includes contributions from
   • The uncertainties and covariances of all the fit parameters in the template functions
   • The uncertainties and covariances of the fitted weights of the template functions
   • The uncertainty on the scale factor alpha, through its effect on the integrals used to determine the signal fraction in the peak region
   • The effect of the uncertainty on the template functions (i.e. the uncertainties and covariences of the fit parameters) on the above mentioned integrals.
2. The uncertainty on the signal fraction due to fitting the residual--equal to the effective number in the residual within the peak region (determined by fitting the residual) divided by the raw number of counts in the peak region
3. The propagation of the uncertainty on the estimate of the background asymmetry.

These are also the same systematics that are estimated for the A_N results.

Note: the background asymmetry has been updated. See this blog. Recall:



Systematics (1) and (2) are then propagated from uncertainties on and systematic (3) is the propagation of the uncertainty on .  The statistical uncertainty is the progated uncertainty from .

pT bin	A_LL	Stat.	Tot. Sys.	Prop.	Res. Fit.	Bkg.
2	-0.002	0.030	0.001	0.000	0.000	0.001
3	-0.023	0.020	0.003	0.001	0.001	0.003
4	0.004	0.021	0.004	0.001	0.000	0.004
5	0.049	0.028	0.007	0.004	0.001	0.005
6	0.000	0.044	0.007	0.001	0.000	0.007
7	0.039	0.060	0.011	0.009	0.001	0.006
8	-0.044	0.072	0.009	0.007	0.000	0.006

Single Spin Plots

Money Plot

Note: for some reason the stat box disappeared at the last moment for the A_L plots.  The current plan is to not explicitly put the plots in the paper, but just reference that they are consistant with zero.  The values are (for A_L blue, A_L yellow and A_LL, respectively)

Fit result: -0.00431399 +/- 0.00682035 chi^2/ndf = 1.04425/6
Fit result: -0.00184262 +/- 0.00636425 chi^2/ndf = 4.43245/6
Fit result: 0.00125572 +/- 0.0112847 chi^2/ndf = 4.85498/6

Note: the A_LL (non-parity violating) is even more consistant with zero than the parity violating single spin asymmetries.

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Cross Section Systematics

Systematic uncertainties on the cross section currently include:

1. Propagation of signal fraction uncertainty--equivelant to (1) for A_LL/A_N
2. Propagation of residual fit--equivelant to (1) for A_LL/A_N
3. Uncertainty on smearing matrix due to MC statistics
4. Uncertainty based on whether to include the 4-5 GeV bin when unfolding
5. Uncertainty on the reconstruction efficiency
6. Uncertainty on the trigger efficiency
7. Uncertainty on the EEMC energy resolution
8. Uncertainty on the EEMC energy scale

The following table lists the statistical and total systematic uncertainties, as well as each of the 8 contributions to the systematic uncertainty.  Note, since the cross section falls rapidly, all the uncertainties in the table are relative uncertainties, i.e. the uncertainties have been divided by the cross section value for the given pT bin.

L.W. pT [GeV/c]	Stat.	Tot. Sys.	Prop.	Res. Fit.	Smearing Matrix	Unf. Range	Reco. Eff.	Trig. Eff.	Energy Res.	Energy Scale
5.457	0.005	0.446	0.001	0.001	0.021	0.295	0.010	0.039	0.052	0.328
6.457	0.007	0.406	0.002	0.002	0.029	0.048	0.010	0.056	0.049	0.395
7.457	0.009	0.373	0.003	0.002	0.036	0.035	0.013	0.080	0.045	0.358
8.457	0.016	0.464	0.007	0.003	0.061	0.010	0.019	0.119	0.043	0.442
9.457	0.023	0.446	0.012	0.003	0.090	0.003	0.028	0.162	0.040	0.401
10.831	0.022	0.627	0.011	0.003	0.095	0.001	0.036	0.152	0.038	0.598
13.382	0.037	1.488	0.022	0.010	0.217	0.003	0.066	0.231	0.034	1.451

The energy scale uncertainty is the dominant systematic.  It is based on a 3% overall uncertainty and computed by locally fitting the cross section to an exponential and integrating +/- 3% of the upper bin edge for each pT bin.  At the lowest pT bin, the effect of whether to include (or not) an additional lower pT bin when unfolding also has a sizeable contribution.

Money Plots