people:walstrom:res [School of Physics and Astronomy Wiki]

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[[extrapolation]]

[[auto_fit]]

{{:groups:cms:walstrom:e100_150.gif|}}\\ 
Fractional resolution as a function of |h|. Also this data shows only the electrons which fit into the energy range (100 < E < 150).Each line corresponds to a different level of pile up. This shows the slope and progression of different levels of pile up as data is taken from low to high |h| values. The final value for Pile up 60 in high |h| was a bad fit and I believe does not represent a physical trend.

{{:groups:cms:walstrom:e150_225.gif|}}\\ 
Shown here is the next energy band up (150 < E < 225). Each energy band is the low end to 150% of the low end, causing the bands to grow in relative range. This plot depects the same fractional energy resolution vs |h| for the same pile up levels. The higher energy energy band has two large effects. Because the range is larger for this set there are more events which fall into it. This causes better fits and reduced errors. Also the general trend that with higher energy electrons the frectional energy difference caused by pile up will be reduced. This is the effect that I sought to quantify.

{{:groups:cms:walstrom:e225_337.gif|}}\\ 
The higher energy band shown here gives electrons with yet higher resolution.

{{:groups:cms:walstrom:e337_506.gif|}}\\ 
This data is as expected fron the hypothesis that highter energy elecrons will have better resolution in the presence of non-trival pile up.

{{:groups:cms:walstrom:e506_759.gif|}}\\ 
Within this energy range pile up 40 at high |h| stays within 5% resolution. 

{{:groups:cms:walstrom:e759_1000.gif|}}\\ 
Within this energy band pile up 60 now stays within 5% resolution. Somewhere around 1 TeV there is a problem with ECAL leaking energy to the HCAL and more sophisticated identification techniques are required.

{{:groups:cms:walstrom:sigma_graph_w80_3.gif|}}\\ 
This is the same data set as above with an additional level of pile up added, 80. This plot is integrated over energy of the electron. Integrating over energy of the electron allows me to break |h| into smaller segments because I am working with a large nubmer of events.

{{:groups:cms:walstrom:chisquare2.gif|}}\\ 
This shows the reduced chi square for the above data. These histrograms do not perfectly fit to gaussian curves and it is difficult to determine if they are fitting as well as they could be. This shows that the fit strength is dancing all over and is not fitting very well. This shows me I must be quite careful when deciding that a gaussian fit accurately.  

{{:groups:cms:walstrom:sigma_graph_hand40_2.gif|}}\\ 
This a set of hand fit histograms showing lower pile up cases. By hand fit I mean I did not use a macro to automatically fit the histogram to a gaussian but used the fitting window to hand fit it. With smaller |h| bins the gap between the barrel and the endcap can be seen as a spike at |h| = 1.5. The data tends to varies more than auto fit plots because the technique is not as consistent from histogram to histogram. 

{{:groups:cms:walstrom:egun_pu40_2.gif|}}\\ 
This plot was generated to explore the intrinsic difference in resolution between two dielectron gun samples. One sample has an energy distrabution from ( 20 < E < 500) while the other has (100 < E < 1000) in GeV. This difference in energy was postulated to cause a difference in intrinsic resolution because background noise will be a different percentage of each sample. This turned out the be the case with the lower energy sample having a slightly worse intrinsic resolution. Each case was done with zero pile up events. The first 10 entries of the lower energy case are zero because there is not data for that |h| range present.
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