Model-independent determination of the strong phase difference between $D^0$ and ${\bar{D}}^0\to {\pi }^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}$ amplitudes

Abstract

For the first time, the strong phase difference between $D^0$ and ${\bar{D}}^0\to {\pi }^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}$ amplitudes is determined in bins of the decay phase space. The measurement uses $818{\mathrm{pb}}^{-1}$ of $e^{+}{e}^{-}$ collision data that is taken at the $\psi (3770)$ resonance and collected by the CLEO-c experiment. The measurement is important for the determination of the $CP$-violating phase $\gamma$ in $B^{\pm }\to D{K}^{\pm }$ (and similar) decays , where the $D$ meson (which represents a superposition of $D^0$ and ${\bar{D}}^0$) subsequently decays to ${\pi }^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}$. To obtain optimal sensitivity to $\gamma$, the phase space of the $D\to {\pi }^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}$ decay is divided into bins based on a recent amplitude model of the decay. Although an amplitude model is used to define the bins, the measurements obtained are model-independent. The $CP$-even fraction of the $D\to {\pi }^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}$ decay is determined to be $F_{+}^{4\pi }=0.769\pm 0.021\pm 0.010$, where the uncertainties are statistical and systematic, respectively. Using simulated $B^{\pm }\to D{K}^{\pm },D\to {\pi }^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}$ decays, it is estimated that by the end of the current LHC run, the LHCb experiment could determine $\gamma$ from this decay mode with an uncertainty of $(\pm 10\pm 7{)}^{\circ }$, where the first uncertainty is statistical based on estimated LHCb event yields, and the second is due to the uncertainties on the parameters determined in this paper.

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Cited by in corpus (10)

• Model-independent determination of the relative strong-phase difference between $D^0$ and ${\bar{D}}^0\to K_{S,L}^0{\pi }^{+}{\pi }^{-}$ and its impact on the measurement of the CKM angle $\gamma /{\varphi }_3$
• Determination of strong-phase parameters in $D\to K_{S,L}^0{\pi }^{+}{\pi }^{-}$
• Measurement of the $CP$-even fraction of $D^0\to {\pi }^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}$
• Measurement of $CP$ observables in the process $B^0\to D{K}^{\ast 0}$ with two- and four-body $D$ decays
• A study of $CP$ violation in the decays $B^{\pm }\to [K^{+}{K}^{-}{\pi }^{+}{\pi }^{-}{]}_D{h}^{\pm }$ ($h=K,\pi$) and $B^{\pm }\to [{\pi }^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}{]}_D{h}^{\pm }$
• Measurement of the $CP$-even fraction of $D^0\to K^{+}{K}^{-}{\pi }^{+}{\pi }^{-}$
• Amplitude analysis of $B^{+}\to \psi (2S)K^{+}{\pi }^{+}{\pi }^{-}$ decays
• Novel correlated $D^0\overline{D}{}^0$ systems for $c/b$ physics and tests of $T/CPT$
• A model-independent measurement of the CKM angle $\gamma$ in the decays $B^{\pm }\to [K^{+}{K}^{-}{\pi }^{+}{\pi }^{-}{]}_D{h}^{\pm }$ and $B^{\pm }\to [{\pi }^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}{]}_D{h}^{\pm }$ ($h=K,\pi$)
• Measurement of the strong-phase difference between $D^0$ and $\overline{D^0}\to K^{+}{K}^{-}{\pi }^{+}{\pi }^{-}$ in bins of phase space