A novel method to measure the relative strong phase between $D^0$ and $\bar{D}^0$ in $D \to K_S^0 \pi^+ \pi^-$ and its application to measurements of the CKM angle $\gamma$ in $B^\pm \to D^0(\bar{D}^0)K^\pm$ decays.

This is the poster presented at the 31st International Symposium on Lepton Photon Interactions at High Energy Physics which took place at Melbourne, Australia 17-21 July 2023.We present a novel unbinned model independent method to measure the relative phase between \(D^0 \to K_S^0\pi^+ \pi^-\) and \(\bar{D}^0 \to K_S^0\pi^+ \pi^-\) (\(\Delta\delta_D\)). We apply this method to the measurement of the CKM angle \(\gamma\) from the decay \(B^\pm \to D(\to K_S^0 \pi^+ \pi^-) K^\pm\). We show that our method has optimal statistical precision and avoid model induced systematic uncertainties associated with mismodelling \(\Delta\delta_D\).