Test 1: Comparison of vertex reconstruction uncertainty (CAT vs TrackIT vs true vertex)

[Shoram444]

GOAL:

To compare the performance of the two tracking algorithms, the old CAT tracking module and the new TrackIT module (working name of Tomas' tracking).

PROCEDURE:

• A data-set of at least 1M events of $2\nu\beta\beta$
• Create histograms and evaluate uncertainty:
  • CAT: 1D histogram of $\Delta y$; where $\Delta y = y_{reco1} - y_{reco2}$ is the difference between the y-components of the reconstructed source foil vertices
  • CAT: 1D histogram of $\Delta z$; where $\Delta z$ is the difference between the z-components of the reconstructed source foil vertices
  • TrackIT: 1D histogram of $\Delta y$; where $\Delta y$ is the difference between the y-components of the reconstructed source foil vertices
  • TrackIT: 1D histogram of $\Delta z$; where $\Delta z$ is the difference between the z-components of the reconstructed source foil vertices
  • CAT vs SIMULATED: 1D histogram of $\Delta y$; where $\Delta y = y_{reco} - y_{simu}$ is the difference between the y-components of the reconstructed vs simulated source foil vertices
  • same as above but z-component
  • same as above but TrackIT vs SIMULATED y-component
  • same as above but TrackIT vs SIMULATED z-component

SIMULATION SETUP:

• Magnetic field off
• 1M events of $2\nu\beta\beta$
• data-cuts: 2 tracks, 2 OM hits, 2 Associated OM hits, 2 foil vertices, Pint>4%, Pext<1%
• for CAT make sure that the reco.conf file only reconstructs "line":
  • in reco.conf file change: fitting_models : string[1] = "line"
• ...

RESULTS:

Plots are saved here

Comparison CAT reconstructed:

For uncertainty in y, z see notebook_1 for analysis.

Overview plot:

Comparison CAT vs Simulated:

For uncertainty in y, z see notebook_2 for analysis.

Overview plot:

COMMENTS AND OTHER STUFF:

Could be interesting in seeing the uncertainty as a function of $E$, $r$, or other..

[miroslav-macko]

I would be interested to make some semi - analytical model for the fitting function. I even have an idea how to try to do that. In my PhD thesis I have shown that Cauchy does not describe this shape perfectly. I proposed some "empirical shape! but maybe this shape can be explained by doing some convolutional integrals. For some inspiration you can have a look at the 4th chapter of my dissertation: https://theses.hal.science/tel-02122290

BTW you can also read there why RMS is bad idea to use. This distribution is cursed, having high dependence on the window you choose to compute the RMS. I discourage to use it. The best is to find a proper fitting function.