Difference between revisions of "Elong-13-05-28"
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===9.2% Systematic Uncertainty=== | ===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 ( | + | From Dustin's work for the proposal, the components to systematic uncertainty make up a relative systematic uncertainty of 9.2%. Plotting this ($\delta A_{zz}^{sys} = 2\left(0.092 \cdot A_{zz}\right)$) as an error band, and propagating it to $b1$, we get the plot below. |
[[Image: 2013-05-28-no_drift_systematics.png]] | [[Image: 2013-05-28-no_drift_systematics.png]] | ||
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===Including Drift=== | ===Including Drift=== | ||
| − | Additionally, there is a compoment due to drift that makes up | + | Additionally, there is a compoment due to drift that makes up $\delta A_{ZZ}^{drift}=\pm \frac{2}{fP_{zz}}\delta \xi = \pm 3.7 \times 10^{-3}$. Including this, $\delta A_{zz}^{sys} = \pm \sqrt{\left(0.092 \cdot A_{zz}\right)^2 + 0.0037^2 }$, the error band expands as in the plot below. |
[[Image: 2013-05-28-with_drift_systematics.png]] | [[Image: 2013-05-28-with_drift_systematics.png]] | ||
| + | |||
| + | The above image is includes the entire $\pm\delta A_{zz}^{sys}$ range. If we only want to show half that (just $\delta A_{zz}^{sys}$ instead of $\pm \delta A_{zz}^{sys}$), it looks like: | ||
| + | |||
| + | [[Image: 2013-05-28-with_half_drift_systematics.png]] | ||
| + | |||
| + | ===Full Error Bars=== | ||
| + | |||
| + | If we put this as $\delta A_{zz} = \sqrt{\delta A_{zz}^{(stat) 2} + \delta A_{zz}^{(sys) 2}}$ as bars on the points, it comes out to the plot below. Our dominating effects are statistics and charge/efficiency fluctuations. | ||
| + | |||
| + | [[Image: 2013-05-28-with_drift_systematics_bars.png]] | ||
| + | |||
| + | The [http://nuclear.unh.edu/~elong/analysis_files/2013-05-16/Azz_error.pdf Rates and Systematic Uncertainty Calculations for a Measurement of $A_{zz}$] tech note has been updated to include this band. | ||
| + | |||
| + | ---- | ||
| + | |||
| + | '''20% Pzz:''' | ||
| + | |||
| + | [[Image: 2013-05-28-pzz-20.png]] | ||
| + | |||
| + | ---- | ||
| + | |||
| + | '''30% Pzz:''' | ||
| + | |||
| + | [[Image: 2013-05-28-pzz-30.png]] | ||
| + | |||
| + | ---- | ||
| + | |||
| + | '''Bouncing between 20% Pzz and 30% Pzz:''' | ||
| + | |||
| + | [[Image: 2013-05-28-pzz-diff.gif]] | ||
| + | |||
| + | --[[User:Ellie|E. Long]] 17:23, 29 May 2013 (UTC) | ||
Latest revision as of 13:51, 18 October 2023
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 ($\delta A_{zz}^{sys} = 2\left(0.092 \cdot A_{zz}\right)$) as an error band, and propagating it to $b1$, we get the plot below.
Including Drift
Additionally, there is a compoment due to drift that makes up $\delta A_{ZZ}^{drift}=\pm \frac{2}{fP_{zz}}\delta \xi = \pm 3.7 \times 10^{-3}$. Including this, $\delta A_{zz}^{sys} = \pm \sqrt{\left(0.092 \cdot A_{zz}\right)^2 + 0.0037^2 }$, the error band expands as in the plot below.
The above image is includes the entire $\pm\delta A_{zz}^{sys}$ range. If we only want to show half that (just $\delta A_{zz}^{sys}$ instead of $\pm \delta A_{zz}^{sys}$), it looks like:
Full Error Bars
If we put this as $\delta A_{zz} = \sqrt{\delta A_{zz}^{(stat) 2} + \delta A_{zz}^{(sys) 2}}$ 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 $A_{zz}$ tech note has been updated to include this band.
20% Pzz:
30% Pzz:
Bouncing between 20% Pzz and 30% Pzz:
--E. Long 17:23, 29 May 2013 (UTC)
