Calculation of Error in Simulation Weighted Asymmetries for Collins Analysis

The first document below (SimulationAsymmetryError_v5.pdf) reviews the proper steps to take to reproduce the error calculation for asymmetries calculated in simulation. These weighted asymmetries, when compared at detector and particle level, give an estimate of the phiC reconstruction systematic.

The plots that accompany the document show some examples of the statistical power. What we have are three weighting schemes:

A_n Vs Z, weighted by Z
A_n Vs pT, weighted by pT
A_n Vs jT, weighted by jT

We have three weighting scenarios for Z: Linear weight, Small weight, and Zero weight. These follow the weighting scheme:

weight = 1 +/- (A_input)*sin(particleLevelPhiC), where

An_zPlus = particleLevelZ;
An_zMinus = -particleLevelZ;
An_PtPlus = particleJetPt/100.;
An_PtMinus = -particleJetPt/100.;
An_JtPlus = particleLevelJt/5.;
An_JtMinus = -particleLevelJt/5.;

for Linear weight. For small weight, which is only done for A_n Vs. Z, I divide the above Z weighting asymmetry by 100. This gives a more realistic visualization of what we would have using a parameterized weight from the data. The zero weight means we set all INPUT ASYMMETRIES to zero, and the weight is really 1 for everything. There are only two weighting scenarios for pT and jT: Linear weight, and zero. 

For more information about the weighting procedure, error analysis procedure, and the "Systematic" plots, see this blog:

What we see from these plots is using the cross ratio method we have large statistical errors, which is very evident from the systematic plots. These systematic plots show the detector asymmetry subtracted from the parameterized particle asymmetry evaluated at the detector level x-value point. For small weight, the errors don't decrease much, and for zero input asymmetry, they're still quite large. In fact, it seems that the errors increase slightly as the weight decreases. The error analysis has been thoroughly reviewed, and the code is working well. This dependence of the errors on the weight seems a little odd, but seems to stem from the fact that our yields are also weighted by the input weight.

What we see is that we would need ~100 times the simulation statistics to have statistically significant difference points on the "systematic" plots. This isn't feasible for computation, so we should investigate a better method. The take-away from this study is regardless of the running period, using the cross ratio asymmetry method in the simulation isn't a viable way to estimate the phiC reconstruction systematic error.