Study of polarised $W\gamma$ production at the LHC

The W $\gamma$-production is a process that can occur in high-energy particle collisions such as those conducted at the LHC. Compared to other weak-boson interactions it has a relatively high cross-section which enables one to study a variety of effects in this process. In this thesis, the W$\gamma$-production is studied based on SHERPA simulations with unpolarised setups as well as with polarised setups. One key area of study is the radiation amplitude zero effect that emerges in all three polarisation states of the W-boson. This effect results in a dip in the pseudorapidity-difference distribution between the charged lepton from the W-decay and the final state photon. This dip is a sensitive phase space region for studying new physics, as it could be filled by several theories, and effects of anomalous couplings in the $WW$$\gamma$-vertex could also be examined. This work will primarily focus on phase space cuts to deepen the dip and make it visible, even with higher-order diagrams that also fill the dip. Additionally, various properties of W-bosons in terms of polarisation will be discussed. This thesis shows that either cuts on a high photon transverse momentum or a cut on the transverse mass of the whole system improves the depth of the dip in the pseudorapidity distribution significantly. With such cuts, the dip is also visible at next to leading order.