## 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

SUSY TTJ

Defining Desired Parameters

  • M3
    • Separating top-top events from background
    • Invariant mass of 3 jets with largest vectorially summed transverse momentum: \[ b^{*}, j_1^{*}, j_2^{*} = \underset{(b, j_1, j_2)}{\arg\max}\; \left|\left|\; p_T(b) + p_T(j_1) + p_T(j_2) \;\right|\right| \] \[ M3 = invariant\_mass\left(b^{*}, j_1^{*}, j_2^{*}\right) \]
    • Most effective with 4+ jets; our data has 6
  • Transverse energy analysis
    • Separating QCD events
    • Most effective with 3 jets → group the data into two systems

Identifying Two Top Quark Systems

  • 2 \(bjj\) groups maximizing transverse momentum
    • \( t \to b + W \to b + 2j \)
  • Calculate M3 for both
  • Calculate M2 for both (invariant mass of jets)
  • Least-squares error (M3 \(\leftrightarrow t\), M2 \(\leftrightarrow W\))
  • Top quark A = Better combination
  • Top quark B = best from rest of system

(Dutta et. al.)

## 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