The purpose of trigonometric axes in plot of electron clusters, ATLAS

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SUMMARY

The discussion centers on the use of trigonometric axes in the plotting of electron clusters resulting from proton-proton collisions at CERN's ATLAS experiment. Specifically, the axes are defined as cos(phi) * tan(theta) for the x-axis and sin(phi) * tan(theta) for the y-axis. This approach allows for consistent angle comparisons across experiments, addressing the challenges posed by the calorimeter's non-zero depth, which could otherwise distort cluster representation. The chosen method effectively minimizes the smearing of clusters that diverge from the interaction point.

PREREQUISITES
  • Understanding of trigonometric functions, specifically sine and cosine.
  • Familiarity with particle physics concepts, particularly electron reconstruction.
  • Knowledge of the ATLAS experiment and its data collection methods.
  • Basic comprehension of the implications of calorimeter depth in particle detection.
NEXT STEPS
  • Research the mathematical foundations of trigonometric transformations in physics.
  • Explore the principles of electron reconstruction techniques in high-energy physics.
  • Study the design and function of the ATLAS calorimeter at CERN.
  • Investigate methods for visualizing particle collision data effectively.
USEFUL FOR

Particle physicists, data analysts in high-energy physics, and researchers involved in the ATLAS experiment will benefit from this discussion, particularly those focused on electron cluster analysis and data visualization techniques.

kimi7335
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Why use trigonometric axes for the plot?
I have been doing some reading on electron reconstruction from proton-proton collisions at CERN. In some of the papers I have read, plots such as the one In the figure are included. What I would like to know is why they have chosen to plot the x and y axes as cos(phi) * tan(theta) and sin(phi) * tan(theta)?
 

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Angles can be compared across experiments, physical dimensions cannot. In addition the calorimeter has some non-zero depth, so just plotting x and y would smear out clusters that point away from the interaction point. You could project everything onto a fixed plane, but that's just extra effort for a less useful result.
 
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