Optimising sensitivity to $\gamma$ with $B^0\to D{K}^{+}{\pi }^{-}$, $D\to K_{\mathrm{S}}^0{\pi }^{+}{\pi }^{-}$ double Dalitz plot analysis

Abstract

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

20 pages, 10 figures

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