\chapter{Introduction}

Modern particle physics pushes mankind's understanding of the fundamental constituents and interactions of our universe by probing matter at the smallest possible length scales. From John Dalton's ``atomic theory," through Rutherford's discovery of the nucleus, up to the construction of the Standard Model, scientists have probed the constituents of matter from the atomic down to sub nucleon level, which is the length scale where quarks and gluons exist within protons and neutrons. 

The Large Hadron Collider is the latest tool with which to measure and discover new physics at the smallest length scale. Four different detectors were built around the accelerator's 27 km circumference. Alice (A Large Ion Collider Experiment) was designed for heavy ion collisions to study quark-gluon plasma. LHCb (LHC beauty) specializes in bottom quark physics and the measurements of CP violating processes. There is Atlas (A Toroidal Lhc ApparatuS). The detector used in this analysis is CMS (Compact Muon Solenoid) constructed 100 meters underground outside the small town of Cessy in the Jura foothills in France. This thesis will briefly describe the LHC (Chapter 2) and the CMS detector (Chapter 3) since multiple reference materials are available on these subjects\cite{LHCTDR} \cite{CMSTDR}. The theoretical motivation for  supersymmetry at the LHC is discussed in chapter 4. 


The main subject of this thesis will be on a search for supersymmetry (SUSY) in the single lepton, with b-tagged jets and missing transverse energy (\met) using 4.98 $fb^{-1}$ of integrated luminosity at the CMS detector (Chapter 5). This analysis is based upon a previously published analysis without the b-tagging requirement\cite{SUS12010}.  The single lepton, with b-tagged jets and \met~ analysis has sensitivity to many SUSY models where bottom (b) quarks participate in the decay cascade. The requirement of a single lepton \footnote{Throughout this thesis, ``lepton" will refer to only electrons and muons unless otherwise specified.} rejects many light flavor hadronic events (QCD) while isolating two predictable backgrounds, \ttbar~ and \wjets~ events.  The analysis requires the event to have at least two b-tagged jets above 40 GeV and four or more total number of jets which are expected from the cascade decays of strongly produced massive SUSY particles such as squarks and gluinos. High \met~ is expected from SUSY signal models due to production of Lightest Supersymmetric Partners (LSP) in R-parity conserving SUSY.

The main background in this analysis is \ttbar~ events that has two separate components, which are predicted separately. The two components are the single lepton events from semileptonic \ttbar~ decays and dilepton-tau events from fully leptonic events or \ttbar~ events involving taus. The dilepton and tau are lumped together since both channels produce additional undetected neutrinos which are predicted by a similar method. The single lepton component is the dominant background in most signal bins, which is predicted by the lepton spectrum method\cite{LeptonSpectrum}. Although the analysis vetoes events with a second identified lepton, two lepton events (dilepton) contribute to our signal bins due to lepton identification inefficiency and detector coverage. There are also contributions from single tau events and lepton plus tau events. The dilepton and tau contributions are predicted by a separate method described in chapter 5. Light flavor hadronic event's (QCD) contribution is expected to be very small, but due to its contribution to our control sample a separate prediction is also made for the QCD contribution. The last and the smallest contribution is from \zjets~ events where one lepton is lost or ignored. This portion of the background is taken from Monte Carlo and found to be negligible. The final prediction is made in bins of \met~ and HT with all the separate components combined. Where HT is defined as the scalar sum of all transverse energy in the jets identified in each event. Since no significant excess was found in the observed data, limits were made in terms of a minimal SUperGRAvity (mSUGRA) SUSY models and Simplified Model Spectra (SMS).
