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

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

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)

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

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

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

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

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

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

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

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”

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

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

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

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

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

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

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

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