## Searching for Supersymmetric Top Quarks at the LHC
[Onkur Sen](http://onkursen.com/single) and [Dr. Paul Padley](http://www.bonner.rice.edu/padley/)
Rice University
[github.com/onkursen/squark-search](http://github.com/onkursen/squark-search)
Motivation and Background
## Why are we doing this?
* LHC: Higgs mass in 125 GeV region
* Standard model: higher loop corrections to Higgs mass diverge quadratically
* "Fine-tuning problem"
* Subtracting two very large numbers
* Another way?
## Supersymmetry (SUSY)
* Main idea: Fermion-boson pairs with same mass, quantum numbers (except spin)
* Partner for boson: -ino
* Partner for fermion: s-
* Higher loops cancel partially
* Logarithmic divergence instead of quadratic
* Interesting note: supersymmetry came from string theory
* Stands on its own as an idea
## Using SUSY
* If supersymmetric partner for top quark exists, higher-order corrections cancel
* Feasibility
* Can only cover some of the parameter space at the current energy level
* Gluinos and heavier stop quarks cannot be detected
* No supersymmetric particle has been discovered yet!
* Searching in the dark
* Not clear that you can ever rule out supersymmetry
* As a result of Higgs experiment, stop quarks are favored to exist
The Stop Quark
Stop quark = top squark = supersymmetric top quark
Expected decay mode:
\[ \tilde{t} \to t + \tilde{\chi}_1^0 \]
where \( \tilde{\chi}_1^0 \) is lightest supersymmetric particle (LSP)
Our goal: use machine learning to optimize the search for this particular decay mode
## The machine learning problem: Classification
## Description
* **Goal**: separating a set of data points into two categories, signal and background
* What's been tried so far?
* Support vector machines (SVMs): Separate data into two classes using a hyperplane that maximizes the "margin"
* Linear discriminant analysis (LDA): Find linear combination of features that best separates data
* Neural Networks: use connected "neurons" with different layers to adapt
Decision trees
Make a yes/no decision based on many factors
Think flowcharts
## Boosting
* Combine many weak learners to make a strong learner
* Ex: "rules of thumb"
* **Supervised learning**: train on data for which the result is known, then apply to new data
* AdaBoost (adaptive boosting): most common boosting algorithm
### Our approach:
### Boosted decision trees
### (BDTs)
## Context
### Theoretical Basis
* [Dutta et al.](http://prd.aps.org/abstract/PRD/v86/i7/e075004) (Texas A&M): proposed search mechanism for stop quarks
* DOI: 10.1103/PhysRevD.86.075004
* Provide phenomenological data that simulates stop quark decays
* Them: Iteratively cut on multiple variables to separate signal from background
* Us: use variables as parameters in BDT
### Experimental Considerations
* In our case, data = **jets**
* Representation of collision result
* 1 jet = 1 final particle
* [PGS4](http://www.physics.ucdavis.edu/~conway/research/software/pgs/pgs4-general.htm)
* Translating data from PYTHIA to objects and jets
* Creates objects by simulating the detector
* BDTs particularly good for Higgs searches
* Framework: [ROOT TMVA](http://tmva.sourceforge.net/)
Outline of Approach
## Getting acquainted
* Used [PYTHIA](http://home.thep.lu.se/~torbjorn/Pythia.html) and [ROOT](http://root.cern.ch/drupal/) to do basic data analysis on particle collisions
* Isolated jets and observed energy distribution
## BDT implementation
* Variables/factors considered
* M3 of top quark A
* M3 of top quark B
* M2 of top quark A
* M2 of top quark B
* Tranverse momentum azimuthal angle of bottom quark
* Tranverse momentum azimuthal angle of 2 jets
* Missing transverse energy
* Train with SUSY as signal, ttj as background
Distributions of Variables
SUSY vs ttj
M3
M3A
M3B
M2
M2A
M2B
Azimuthal Angles
Bottom Quark
Jet 1
Jet 2
BDT Results
Classification of Signal and Background
Signal
Background
BG Rejection vs. SIG Efficiency
Better than cut and count!
Test vs. Training
Test
Training
We're not overtraining!
## Future work
* Larger data sets to corroborate results
* Test multiple SUSY points
* Examine individual decision trees more precisely to determine viability of approach
* Fine tuning in efficiency
## Potential
If this project succeeds we can:
* Strongly suggest the evidence of a supersymmetric particle
* Detect it now within the current parameter space
* Provide a possible partial solution to the fine-tuning problem in the Higgs context
## Acknowledgments
* Dr. Paul Padley
* Kuver Sinha and Bhaskar Dutta
* Robert Brockman
* Family, friends