Uncertainty

Uncertainty Study

Uncertainty

Table 1: Data Cut Uncertainty
Variable	Standard Cut	Varied Cut	Data Set	Difference from nominal value
zVertex	abs(zVertex) < 50 0.1 < y < 0.5	zVertex > 0	MinBias	0.0422
zVertex	abs(zVertex) < 50 0.1 < y < 0.5	zVertex > 0	Topology	-0.1883
	abs(zVertex) < 50 0.5 < y < 1.0	zVertex > 0	MinBias	0.1526
	abs(zVertex) < 50 0.5 < y < 1.0	zVertex > 0	Topology	-0.323
	abs(zVertex) < 50 0.1 < y < 0.5	zVertex < 0	MinBias	0.1188
	abs(zVertex) < 50 0.1 < y < 0.5	zVertex < 0	Topology	0.0379
	abs(zVertex) < 50 0.5 < y < 1.0	zVertex < 0	MinBias	0.0454
	abs(zVertex) < 50 0.5 < y < 1.0	zVertex < 0	Topology	0.414

The minbias analysis with standard cuts can be found here

The topology analysis with standard cuts can be found here

The nominal rapidity cut, 0.1 < y < 0.5, was chosen such that cosmic ray candidates could be cut from the data sample. However the interference is most pronounced at midrapidity. Loosening the cut for the minbias data set is reasonable, considering that cosmics would have to pass through the zdc's coincidentally to satisfy the trigger. Hence, the benefit of loosening the cut seems to outweigh the minimal impact of cosmic ray contamination.

Rapidity

0.1 < y < 0.5

0.0 < y < 0.5

MinBias

0.0935

After reading through Vladimir Morozov's section on systematic errors and looking up Falk Meissner's page I've come up with a possible summary table:

Source	Summary
Trigger	F. Meissner asseses this at < 1% according to the ZDC paper and hadron yield paper. At the moment I'm not sure what to make of this.
Tracking	V. Morozov "compared the ratio of N_hits to the number of possible hits on the track N_{possible hits} in data and MC. The number of possible hits was calculated by extrapolating a track's geometry over the pad plane. The calculation incorporated both the detector geometry and features of the track finding routine....The quality of the track fit in data and MC is characterized by the &chi² per d.o.f of the track fit...In a related analysis the authors studied the variation in the tracking efficiency-corrected p_T and &eta spectra due to small variations in track quality cuts. The systematic error was found to be 6.4% for each reconstructed track, which we accept as a tracking efficiency systematic error for the present analysis." Still looking up the reference. I don't know if it applicable in this analysis or if an analogous study exists. F. Meissner has a quote of 4% per track which he explains by: hadron yield paper: 70-95% (p_T= 0.1-2GeV), with 85% for p_T>0.2 compares well to values obtained from the rho Monte Carlo, see here
Vertex Finding	V. Morozov says he plots "invariant mass spectra for identified secondary e⁺e^- pairs comprised of any two global tracks and for pairs comprised of two global tracks that also were primary tracks...The ratio of the e⁺e^- pairs with primary tracks to the total number of pairs gives an estimate of the vertex finding efficiency in the data." He comes up with an 8.5% estimate of the error in vertex finding efficiency. F. Meissner has a quote of 8% which he explains by: Compare LMV and DCA for the rho MC, see here
Pair Identification	V. Morozov estimates the "systematic uncertainty in pair identification efficiency via specific energy loss". He goes through a rigorous mathematical justification to come up with an estimate of 2% which ends up being negligible in comparison to the statistical error. I'm not sure this is directly applicable to this analysis as he is looking at e⁺e^- pairs and we are looking at &pi⁺&pi^-pairs
p_T Mis-Reconstruction	Morozov says in order "to study the systematic error due to shift in reconstructed p_T^reco compared to the true value of transverse momenta," he re-computes "the reconstruction effficienty without applying the shift correction to the simulations. The raw M_inv distribution (which is computed with p_T correction) is then efficiency-corrrected with two different efficiency functions - one with account of p_T shift, and the other without." Subsequently, using the error of the pT correction to be ~10% he estimates the error due to the p_T distortion to be ~2%.
Asymmetry	To estimate whether the number of reconstructed tracks in the East vs. West side of the TPC is different Morozov computes the ratio: A = (N₊₊ - N_--)/(N₊₊ + N_--) x (N₊₊ + N_--)/(N₊₊ + N_-- + N_+-) where N₊₊ is the number of events in the identified pool of events with two tracks with positive p_z . The ratio ends up being within 2&sigma of zero, and therefore not appreciable. This may be akin to my own zVertex studies.
Sensitivity to Generated Spectra	Morozov attempts to account for the possibility that the physics model of the event generator is wrong. "To test the sensitivity of reconstruction efficienty to variations in generated spectra, we can generate an event sample with, for instance, flat p_T^tot pass this event sample through the GEANT simulation, event reconstruction and analysis, and determine reconstruction efficiency in that way. Alternatively, we can use the same event generator event sample that we have been using so far(with pair transverse momentum distributed according to the probability distribution f(p_T^tot)), but compute the efficiency by the formula: Reconstruction Efficiency From Flat p_T^tot Spectrum = = # weighted events after detector simulation and all analysis cuts / # weighted generated events in acceptance" where the weight for each event is inversely proportional to f(p_T^tot)). He ultimately determines that the reconstruction efficiency "is not affected by the shape of the generated distribution" for most values of the transverse momentum.
Varying All Analysis Cuts	Morozov varied all cuts by ± 2.5% ± 5.0% ± 10%. He ultimately determined that "the relative numer variations were found to be very close (differ on the average by ~ 4.5%) in data and simulations, therefore the simulations describe the data response to the analysis cuts with excellent accuracy". Meissner did a cut variation study to which he attributed a 5% systematic error. Supporting plots here.