Amplitude Analysis of $D^+ \rightarrow K^- K^+ \pi^+$ Decay with LHCb 2012 Data and RF-foil Simulations for the LHCb Upgrade

The $D^{+} \to K^{-}K^{+}\pi^{+}$ decay is a hadronic process dominated by resonant intermediate states. In order to quantify and understand the nature of each contribution, an amplitude analysis must be performed. The most common approach for this task is the Isobar Model, where each resonant contribution is described by a combination of Breit-Wigner functions, form factors and angular distribution functions. Achieving a precise description using the Isobar model is a challenging task since it does not provide an adequate framework for broad, overlapping structures typical from the S-wave amplitudes. Due to the huge statistics provided by LHCb, subtle effects might become relevant to our model. The LHCb experiment is going through an upgrade process for the next LHC run period. LHC will provide a much higher luminosity and all subsystems are required to upgrade in order to improve the experiment performance and make good use of the available data. The Vertex Locator, in particular, will be upgraded to a hybrid pixel detector and a new RF foil design is required for this. In this thesis, we show the first Isobar fit results for this channel using the 2012 LHCb data sample and simulation studies for the upgrade of the RF foil in order to achieve the best performance as possible.