1. Data Analysis in Particle Physics
December 1, 2010
Timothy Harrington-Taber

2. Data Analysis in Particle Physics
Historical Review
What we get from the detector
Pre-processing of data
Cutting and fitting
Monte Carlo simulations

3. History of Particle Data Analysis
Essentially limited by detectors
Manual count of scintillator hits (early 1900’s)
Cloud chamber (1930’s)
Bubble chamber (1950’s)

4. Particle Track Tracing
Bubble and cloud chambers provided excellent information about the path of the particle, but the photographs typically had to be manually examined to obtain physical information about ionizing particles.
Time-consuming to analyze and produce

5. Directly Available Information
At the fundamental level, detectors provide information about where particles were found when.
Momentum, energy, charge, etc. are usually derived based on “reading” these measurements based on our knowledge of the detector

6. Event Reconstruction
Detector hits are reconstructed into tracks that best explain the pattern observed
Sometimes, one particle is reconstructed as two separate tracks… or two particles are reconstructed as only one track
Energy, momentum, and charge associated with the track is recorded, along with track length and position of origin

7. Data Profile
With the charge, momentum, energy and decay length of the track, the reconstruction software can determine the likelihood of the track being caused by a specific particle
Other information available includes the number of hits assigned to the track in a given detector, its isolation from other tracks, and missing energy/momentum in the collision

8. Analyzing Data No longer done by hand
Specialized computer software filters and analyzes events for patterns of interest
ROOT Data Analysis Framework is described as a set of object-oriented frameworks, usable within C++, optimized for particle physics work

9. Example of using ROOT
Declare the process of interest (decay of B-meson to J/ψ ππK with J/ψ decaying to two muons)
Run script to filter those reconstructed particles matching this pattern to make available a smaller file containing only events roughly matching criteria

10. Cutting and Fitting
Not all events that pass a filter will be the process or particle intended
Leaving out certain events based on values of particular parameters (cutting) allows for better identification of the particle/decay in question
Typically, the cut data can be fit to a “signal” distribution and a “background” distribution

11. Fitting Procedure
Most often, data is plotted as a histogram with the number of counts per bin on the vertical axis and the relevant variable on the horizontal (e.g. Energy or Momentum)
ROOT can be used to determine background and signal fits, giving numbers of events to each distribution included in the fit
3σ signifies “evidence”, 5σ is a “discovery”

12. Significance
Another measure of the strength of the signal is known as the significance
This measures the amount of signal S to the amount of background B
Significance
Integrated over the region near the peak of the signal

13. Example (continued)
This file will still probably be too large to use reasonably
Apply preliminary cuts, and filter data to only include parameters that might be used in the optimization process
Note: leaving out a parameter will require repeating this step if later optimization requires its use

14. Optimization of Fit Parameters
Set up a script that will step through several values of a particular cut (leaving others fixed) and return the significance for each value
Repeat for other optimization parameters
Adjust fixed values of optimization parameters based on previous round of analysis (plotting data now is a good idea as a check)
Repeat until no longer able to improve significance

15. Understanding the data
Certain processes other than those directly studied may pass the cuts used
Measured values from previous experiment may be used to predict parameters that we expect to observe, or to provide expected cross-sections based on particular unknowns present in the data

16. Monte Carlo Analysis
One of the strongest tools in determining likely detector response to physical processes is to perform a Monte Carlo simulation
A Monte Carlo simulation randomly and repeatedly selects parameters from a specified domain and uses them to create its results

17. Monte Carlo in Particle Physics
In particle physics, a decay particle and decay mode are specified
Angular distribution and subsequent decays are determined randomly within specified boundaries
Interaction with the detector is also treated randomly (where the process is random), and the reconstruction algorithm is applied

18. Monte Carlo Usage
The Monte Carlo model of the process can be compared to the data obtained
Most detectors have existing Monte Carlo simulations of “background” events of various kinds to assist in the measurement of cross-section of a particular process

19. Data Analysis History Types of Data Obtainable Event Reconstruction
Cutting and Fitting
Brief Overview of Monte Carlo methods