Model independent determination of the CKM phase $\gamma$ using input from $D^0-{\bar{D}}^0$ mixing

Abstract

We present a new, amplitude model-independent method to measure the CP violation parameter $\gamma$ in $B^{-}\to D{K}^{-}$ and related decays. Information on charm interference parameters, usually obtained from charm threshold data, is obtained from charm mixing. By splitting the phase space of the $D$ meson decay into several bins, enough information can be gained to measure $\gamma$ without input from the charm threshold. We demonstrate the feasibility of this approach with a simulation study of $B^{-}\to D{K}^{-}$ with $D\to K^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}$. We compare the performance of our novel approach to that of a previously proposed binned analysis which uses charm interference parameters obtained from threshold data. While both methods provide useful constraints, the combination of the two by far outperforms either of them applied on their own. Such an analysis would provide a highly competitive measurement of $\gamma$. Our simulation studies indicate, subject to assumptions about data yields and the amplitude structure of $D^0\to K^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}$, a statistical uncertainty on $\gamma$ of $\sim 12^{\circ }$ with existing data and $\sim 4^{\circ }$ for the LHCb-upgrade.

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• A model-independent Dalitz plot analysis of $B^{\pm }\to D{K}^{\pm }$ with $D\to K_{\mathrm{S}}^0{h}^{+}{h}^{-}$ ($h=\pi ,K$) decays and constraints on the CKM angle $\gamma$
• Measurement of phi_3 with Dalitz Plot Analysis of B->D(*)K Decay
• Model-independent search for CP violation in D0 to K-K+pi-pi+ and D0 to pi-pi+pi+pi- decays
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• New determination of the D0->K-pi+pi0 and D0->K-pi+pi+pi- coherence factors and average strong-phase differences
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Cited by in corpus (12)

• Amplitude Analyses of $D^0\to {\pi }^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}$ and $D^0\to K^{+}{K}^{-}{\pi }^{+}{\pi }^{-}$ Decays
• First observation of $D^0-{\bar{D}}^0$ oscillations in $D^0\to K^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}$ decays and measurement of the associated coherence parameters
• CP violation in the B system
• Contributions to the width difference in the neutral $D$ system from hadronic decays
• Amplitude analysis of $D^0\to K^{-}{\pi }^{+}{\pi }^{+}{\pi }^{-}$
• Model-independent determination of the strong phase difference between $D^0$ and ${\bar{D}}^0\to {\pi }^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}$ amplitudes
• Dispersive analysis of neutral meson mixing
• Improved sensitivity to the CKM phase $\gamma$ through binning phase space in $B^{-}\to D{K}^{-}$, $D\to K^{+}{\pi }^{-}{\pi }^{-}{\pi }^{+}$ decays
• Measurement of the CKM angle ${\phi }_1$ in $B^0\to \bar{D}{}^{(\ast )0}{h}^0$, $\bar{D}{}^0\to K_S^0{\pi }^{+}{\pi }^{-}$ decays with time-dependent binned Dalitz plot analysis
• Recent advances in charm mixing and $CP$ violation at LHCb
• A method for model-independent measurement of the CKM angle $\beta$ via time-dependent analysis of the $B^0\to D{\pi }^{+}{\pi }^{-}$, $D\to K_S^0{\pi }^{+}{\pi }^{-}$ decays
• A novel unbinned model-independent method to measure the CKM angle $\gamma$ in $B^{\pm }\to D{K}^{\pm }$ decays with optimised precision