Unbinned model-independent measurements with coherent admixtures of multibody neutral $D$ meson decays

Abstract

Various studies of Standard Model parameters involve measuring the properties of a coherent admixture of $D^0$ and ${\overline{D}}^0$ states. A typical example is the determination of the Unitarity Triangle angle $\gamma$ in the decays $B\to DK$, $D\to K_S^0{\pi }^{+}{\pi }^{-}$. A model-independent approach to perform this measurement is proposed that has superior statistical sensitivity than the well-established method involving binning of the $D\to K_S^0{\pi }^{+}{\pi }^{-}$ decay phase space. The technique employs Fourier analysis of the complex phase difference between $D^0$ and ${\overline{D}}^0$ decay amplitudes and can be easily generalised to other similar measurements, such as studies of charm mixing or determination of the angle $\beta$ from $B^0\to D{h}^0$ decays.

Comments: 24 pages, 6 figures; Updated with published version