A Method to Measure $\phi_1$ Using $\bar{B}^0 \to D h^0$ With Multibody $D$ Decay

We describe a new method to measure the angle $\phi_1$ 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 $2\phi_1$, and thus resolve the ambiguity between $2\phi_1$ and $\pi-2\phi_1$ in the measurement of $\sin(2\phi_1)$ using $\bar{B}^0 \to J/ \psi \ks$. We present a feasibility study of this method using Monte Carlo simulation.