A Method to Measure ${\varphi }_1$ Using ${\bar{B}}^0\to D{h}^0$ With Multibody $D$ Decay

We describe a new method to measure the angle ${\varphi }_1$ of the CKM Unitarity Triangle using amplitude analysis of the multibody decay of the neutral $D$ meson produced via $\bar{B}\to D{h}^0$ colour-suppressed decays. The method employs the interference between $D^0$ and ${\bar{D}}^0$ to directly extract the value of $2{\varphi }_1$, and thus resolve the ambiguity between $2{\varphi }_1$ and $\pi -2{\varphi }_1$ in the measurement of $\sin (2{\varphi }_1)$ using ${\bar{B}}^0\to J\mathrm{/}\psi \text{ks}$. We present a feasibility study of this method using Monte Carlo simulation.