Study of CP violation in $B^\pm$ decays to $\overline{D^0}(D^0) K^\pm$ at FCCee

The great progress made recently in the sector of Flavor Physics has enabled to establish CP violation in the B-meson decays. The unitarity triangle derived from the unitarity relation $V_{ub}^* V_{ud} + V_{cb}^* V_{cd} + V_{tb}^* V_{td} = 0$ has been measured very precisely. To further asses our understanding of CP violation, it would be useful to carry out similar measurement of other triangles. In this note, we investigate the triangle derived from the relation $V_{ub}^* V_{us} + V_{cb}^* V_{cs} + V_{tb}^* V_{ts} = 0$. Two angles of this triangle ($\alpha_s$ and $\beta_s$) could be measured very accurately at FCCee using the decays $B_s(\overline{B_s})\rightarrow D^\pm_sK^\mp$ and $B_s(\overline{B_s})\rightarrow J/\psi \phi$ respectively, as discussed elsewhere by us. This note concentrates on the measurement of the third angle $\gamma_s$ using the modes $B^\pm \to \overline{D^0}(D^0)K^\pm$. We show that a direct measurement of the angle $\gamma_s$ is possible with some specific $B^\pm$ decays with an estimated resolution of the order of 1$^\circ$.