Optimising sensitivity to ${\hat{I}}^3$ with $B^0\to D{K}^{+}\ddot{I}{€}^{-}$, $D\to K_{\mathrm{S}}^0\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ double Dalitz plot analysis

Abstract

Two of the most powerful methods currently used to determine the angle ${\hat{I}}^3$ of the CKM Unitarity Triangle exploit $B^{+}\to D{K}^{+}$, $D\to K_{\mathrm{S}}^0\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ decays and $B^0\to D{K}^{+}\ddot{I}{€}^{-}$, $D\to K^{+}{K}^{-}$, $\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ decays. It is possible to combine the strengths of both approaches in a "double Dalitz plot" analysis of $B^0\to D{K}^{+}\ddot{I}{€}^{-}$, $D\to K_{\mathrm{S}}^0\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ decays. The potential sensitivity of such an analysis is investigated in the light of recently published experimental information on the $B^0\to D{K}^{+}\ddot{I}{€}^{-}$ decay. The formalism is also expanded, compared to previous discussions in the literature, to allow $B^0\to D{K}^{+}\ddot{I}{€}^{-}$ with any subsequent $D$ decay to be included.

20 pages, 10 figures