Measurement of the Polarisation of the W Boson and Application to Supersymmetry Searches at the Large Hadron Collider

This thesis gives an account of two analyses performed using data from the Compact Muon Solenoid experiment at the Large Hadron Collider. The first analysis measures the polarisation of $W$ bosons with large transverse momentum using 36 pb$^{-1}$ of data collected in 2010. The second applies similar techniques to a search for supersymmetry in events containing a single lepton, jets and missing transverse energy. This analysis utilises 1.14 fb$^{-1}$ of data collected up to 2011. Background material related to the Standard Model, supersymmetry and the experimental apparatus are reviewed in detail. The $W$ polarisation measurement is performed in both the $W\longrightarrow e\nu$ and $W\longrightarrow\mu\nu$ channels. The expected effect, a large dominance of the left-handed over the right-handed helicity state, is observed with a significance of $7.8\sigma$ for the $W^+$ and $5.1\sigma$ for the $W^-$ in the muon channel. Similar results are found in the electron channel and for a combined fit to both lepton channels. The second analysis conducts a search for supersymmetry in events containing a single lepton, jets and missing transverse energy. The search employs techniques developed for the $W$ polarisation measurement to separate supersymmetry from Standard Model backgrounds. No deviation from the Standard Model is observed. A detailed statistical interpretation is performed and used to set limits within the Constrained Minimal Supersymmetric Standard Model as well as two simplified models.