Implications of Recent ${\bar{B}}^0\to D^{(\ast )0}{X}^0$ Measurements

Abstract

The recent measurements of the color-suppressed modes ${\bar{B}}^0\to D^{(\ast )0}{\pi }^0$ imply non-vanishing relative final-state interaction (FSI) phases among various $\bar{B}\to D\pi$ decay amplitudes. Depending on whether or not FSIs are implemented in the topological quark-diagram amplitudes, two solutions for the parameters $a_1$ and $a_2$ are extracted from data using various form-factor models. It is found that $a_2$ is not universal: $|a_2(D\pi )|=0.40-0.55$ and $|a_2(D^{\ast }\pi )|=0.25-0.35$ with a relative phase of order $(50-55{)}^{\circ }$ between $a_1$ and $a_2$. If FSIs are not included in quark-diagram amplitudes from the outset, $a_2^{eff}/a_1^{eff}$ and $a_2^{eff}$ will become smaller. The large value of $|a_2(D\pi )|$ compared to $|a_2^{eff}(D\pi )|$ or naive expectation implies the importance of long-distance FSI contributions to color-suppressed internal $W$-emission via final-state rescatterings of the color-allowed tree amplitude.

Comments: 17 pages. The Introduction is substantially revised and the order of the presentation in Sec. 2 is rearranged. To appear in Phys. Rev