Study of CKM angle $\gamma$ sensitivity using flavor untagged $B^0_s\rightarrow \tilde{D}^{(*)0}\phi$ decays

A sensitivity study for the measurement of the CKM angle $\gamma$ from $B^0_s\rightarrow \tilde{D}^{(*)0}\phi$ decays is performed using $D$ meson reconstructed in the quasi flavour-specific modes $K\pi$, $K3\pi$, $K\pi\pi^0$, and \CP-eigenstate modes $KK$ and $\pi\pi$, where the notation $\tilde{D}^0$ corresponds to a $D^0$ or a ${\tilde{D}^0}$ meson. The LHCb experiment is taken as a use case. A statistical uncertainty of about $8-19^{\circ}$ can be achieved with the $pp$ collision data collected by the LHCb experiment from year 2011 to 2018. The sensitivity to $\gamma$ should be of the order $3-8^{\circ}$ after accumulating 23\invfb of $pp$ collision data by 2025, while it is expected to further improve with 300~fb$^{-1}$ by the second half of the 2030 decade. The accuracy depends on the strong parameters $r^{(*)}_{B}$ and ${\delta^{(*)}_{B}}$, describing, together with $\gamma$, the interference between the leading amplitudes of the $B^0_s\rightarrow \tilde{D}^{(*)0}\phi$ decays.