Measurement of branching-fraction ratios and $CP$ asymmetries in $B^{\pm} \to D_{CP\pm}K^{\pm}$ decays at Belle and Belle II

TL;DR

This paper measures $CP$ asymmetries and branching ratios in $B^{ m ext{±}} o D_{CP}^ ext{ ext{±}}K^ ext{ ext{±}}$ decays, combining data from Belle and Belle II, to constrain the CKM angle $oldsymbol{\phi_3}$ with improved precision.

Contribution

It provides the first combined analysis of Belle and Belle II data for these decays, offering new constraints on the CKM angle $oldsymbol{\phi_3}$ and $r_B$ with reduced uncertainties.

Findings

Measured $CP$ asymmetries: $oldsymbol{\mathcal{A}_{CP+} = +12.5 ext{ extpm}5.8 ext{ extpm}1.4 ext{ extpercent}}$ and $oldsymbol{\mathcal{A}_{CP-} = -16.7 ext{ extpm}5.7 ext{ extpm}0.6 ext{ extpercent}}$.

Determined branching fraction ratios: $oldsymbol{\mathcal{R}_{CP+} = 1.164 ext{ extpm}0.081 ext{ extpm}0.036}$ and $oldsymbol{\mathcal{R}_{CP-} = 1.151 ext{ extpm}0.074 ext{ extpm}0.019}$.

Constrained the CKM angle $oldsymbol{\phi_3}$ to specific intervals with improved confidence.

Abstract

We report results from a study of $B^\pm \rightarrow DK^\pm$ decays followed by $D$ decaying to $CP$~eigenstates, where $D$ indicates a $D^0$ or $\bar{D}^{0}$ meson. These decays are sensitive to the Cabibbo-Kobayashi-Maskawa unitarity-triangle angle $\phi_{3}$. The results are based on a combined analysis of the final data set of $772 \times 10^6~B\bar{B}$ pairs collected by the Belle experiment and a data set of $198 \times 10^6~B\bar{B}$ pairs collected by the Belle~II experiment, both in electron-positron collisions at the $\Upsilon(4S)$ resonance. We measure the $CP$ asymmetries to be $\mathcal{ A}_{CP +} =~(+12.5 \pm 5.8 \pm 1.4)\% $ and $\mathcal{ A}_{CP -} =~(-16.7 \pm 5.7 \pm 0.6)\%$, and the ratios of branching fractions to be $\mathcal{ R}_{CP+}=~1.164 \pm 0.081 \pm 0.036 $ and $\mathcal{ R}_{CP-} =~1.151 \pm 0.074 \pm 0.019$. The first contribution to the uncertainties is statistical, and the second is systematic. The asymmetries $\mathcal{A}_{CP +}$ and $\mathcal{A}_{CP -}$ have similar magnitudes and opposite signs; their difference corresponds to 3.5~standard deviations. From these values we calculate 68.3\% confidence intervals of ($8.5^{\circ}<\phi_{3}<16.5^{\circ}$) or ($84.5^{\circ}<\phi_{3}<95.5^{\circ}$) or ($163.3^{\circ}<\phi_{3}<171.5^{\circ}$) and $0.321<r_{B}<0.465$.