Optimizing sensitivity to γ with B0→DK+π−, D→KS0π+π− double Dalitz plot analysis
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Abstract
Two of the most powerful methods currently used to determine the angle $\ensuremath{\gamma}$ of the CKM Unitarity Triangle exploit ${B}^{+}\ensuremath{\rightarrow}D{K}^{+}$, $D\ensuremath{\rightarrow}{K}_{S}^{0}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ decays and ${B}^{0}\ensuremath{\rightarrow}D{K}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$, $D\ensuremath{\rightarrow}{K}^{+}{K}^{\ensuremath{-}}$, ${\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ decays. It is possible to combine the strengths of both approaches in a ``double Dalitz plot'' analysis of ${B}^{0}\ensuremath{\rightarrow}D{K}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$, $D\ensuremath{\rightarrow}{K}_{S}^{0}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ decays. The potential sensitivity of such an analysis is investigated in the light of recently published experimental information on the ${B}^{0}\ensuremath{\rightarrow}D{K}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ decay. The formalism is also expanded, compared to previous discussions in the literature, to allow ${B}^{0}\ensuremath{\rightarrow}D{K}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ with any subsequent $D$ decay to be included.
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