Amplitude analysis of $D^0\rightarrow K^+K^-\pi^+\pi^-$ and its subsequent use in measuring the CKM phase $\gamma$ through $B^{\pm}\rightarrow D(\rightarrow K^+K^-\pi^+\pi^-)K^{\pm}$ decays at LHCb

An amplitude analysis of the 4-body charmed decay $D^0\rightarrow K^+K^-\pi^+\pi^-$ has been performed using data collected from symmetric electron-positron collisions at the CLEO experiment. Both flavour tagged and CP tagged data are utilised in the analysis, making it unique among amplitude analyses performed at other experiments and providing extra sensitivity to the phases of the amplitude components. This analysis uses a data driven regularisation method to determine which of the multitude of possible amplitude components to include in the amplitude model. The dominant contributions are found to be $D^0 \to \phi(1020) \, \rho^0(770)$, $D^0 \to K^- \, K_{1}(1270)^{+}$ and $D^0 \to K^- \, K_{1}(1400)^{+}$. Tests for CP violation in the $D$ system are performed using the amplitude model; no evidence for CP violation is found. The amplitude model obtained is crucial input for a model-dependent measurement of the CP-violating phase $\gamma$ using $B^\pm \to D(\to K^+K^-\pi^+\pi^-)K^\pm$ decays, which remains one of the least constrained parameters of the Standard Model. Significant progress has been made towards this measurement using the full Run 1 LHCb dataset corresponding to 3 fb$^{-1}$ of integrated luminosity. This includes: data selection including the use of a multivariate classifier, fits to mass distributions to obtain event-by-event signal and background weights and an investigation into potential biases in the extraction of $\gamma$ from $B^\pm \to D(\to K^+K^-\pi^+\pi^-)K^\pm$ decays using the control channel $B^\pm \to D(\to K^+K^-\pi^+\pi^-)\pi^\pm$.