CP violation and material interaction of neutral kaons in measurements of the CKM angle $\gamma$ using $B^\pm\to DK^\pm$ decays where $D\to K_\text{S}^0\pi^+\pi^-$
As measurements of the CKM angle $\gamma$ in decays of $b$-hadrons become increasingly precise, it is important to consider the impact of processes that affect secondary and tertiary decay products and can contribute to the observed CP violation. The golden decay mode used to measure $\gamma$ is $B^\pm\to DK^\pm$, where $D\to K_\text{S}^0\pi^+\pi^-$. Due to the presence of a $K_\text{S}^0$ meson in the final state, $\gamma$ measurements based on this mode are affected by neutral kaon CP violation and matter regeneration, and this study examines the potential size of the impact. Previous studies determine the impact of kaon CP violation to be a few degrees in size, but make simplifying assumptions about how experimental measurements are implemented. These assumptions are lifted in the present study, and the matter regeneration effect is included for the first time. The results are presented within the context of $\gamma$ measurements to be made using the LHCb and Belle II II detectors. It is found that the expected biases due to ignoring the effects of CP violation and matter regeneration in neutral kaons is small and less than $0.5^\circ$ degrees in all experimental scenarios considered.