Elong-13-05-28

Systematic Error Bars

9.2% Systematic Uncertainty

From Dustin's work for the proposal, the components to systematic uncertainty make up a relative systematic uncertainty of 9.2%. Plotting this (<math>\delta A_{zz}^{sys} = 2\left(0.092 \cdot A_{zz}\right)</math>) as an error band, and propagating it to <math>b1</math>, we get the plot below.

Including Drift

Additionally, there is a compoment due to drift that makes up <math>\delta A_{ZZ}^{drift}=\pm \frac{2}{fP_{zz}}\delta \xi = \pm 3.7 \times 10^{-3}</math>. Including this, <math>\delta A_{zz}^{sys} = 2\sqrt{\left(0.092 \cdot A_{zz}\right)^2 + 0.0037^2 }</math>, the error band expands as in the plot below.

The above image is includes the entire <math>\pm\delta A_{zz}^{sys}</math> range. If we only want to show half that, it looks like:

Full Error Bars

If we put this as <math>\delta A_{zz} = \sqrt{\delta A_{zz}^{(stat) 2} + \delta A_{zz}^{(sys) 2}}</math> as bars on the points, it comes out to the plot below. Our dominating effects are statistics and charge/efficiency fluctuations.

The Rates and Systematic Uncertainty Calculations for a Measurement of <math>A_{zz}</math> tech note has been updated to include this band.

--E. Long 17:23, 29 May 2013 (UTC)