First measurement of the CKM angle $\phi_3$ with $B^{\pm}\to D(K_{\rm S}^0\pi^+\pi^-\pi^0)K^{\pm}$ decays

TL;DR

This paper reports the first model-independent measurement of the CKM angle φ₃ using B±→D(Kₛ⁰π⁺π⁻π⁰)K± decays, utilizing CLEO-c data for strong-phase differences and the full Belle dataset, resulting in a measurement consistent with the world average.

Contribution

It introduces a novel model-independent approach to measure φ₃ using multibody D decays and CLEO-c strong-phase inputs, based on the full Belle dataset.

Findings

Measured φ₃ as (5.7^{+10.2}_{-8.8} ± 3.5 ± 5.7)°

Determined the amplitude ratio r_B as 0.323 ± 0.147 ± 0.023 ± 0.051

95% confidence interval on φ₃ is (-29.7°, 109.5°)

Abstract

We present the first model-independent measurement of the CKM unitarity triangle angle $\phi_3$ using $B^{\pm}\to D(K_{\rm S}^0\pi^+\pi^-\pi^0)K^{\pm}$ decays, where $D$ indicates either a $D^{0}$ or $\overline{D}^{0}$ meson. Measurements of the strong-phase difference of the $D \to K_{\rm S}^0\pi^+\pi^-\pi^0$ amplitude obtained from CLEO-c data are used as input. This analysis is based on the full Belle data set of $772\times 10^{6}$ $B\overline{B}$ events collected at the $\Upsilon(4S)$ resonance. We obtain $\phi_3 = (5.7~^{+10.2}_{-8.8} \pm 3.5 \pm 5.7)^{\circ}$ and the suppressed amplitude ratio $r_{B} = 0.323 \pm 0.147 \pm 0.023 \pm 0.051$. Here the first uncertainty is statistical, the second is the experimental systematic, and the third is due to the precision of the strong-phase parameters measured from CLEO-c data. The 95% confidence interval on $\phi_3$ is $(-29.7,~109.5)^{\circ}$, which is consistent with the current world average.