Measurement of branching fractions and $CP$ violation parameters in $B\to \omega K$ decays with first evidence of $CP$ violation in $B^0\to \omega K_s^0$

We present a measurement of the branching fractions and charge-parity-($CP$-)violating parameters in $B\to \omega K$ decays. The results are obtained from the final data sample containing $772\times {10}^6$ $B\overline{B}$ pairs collected at the $\mathrm{{\rm Y}}(4S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider. We obtain the branching fractions $\mathcal{B}(B^0\to \omega K^0)=(4.5\pm 0.4(\text{stat})\pm 0.3(\text{syst}))\times {10}^{-6},\mathcal{B}(B^{+}\to \omega K^{+})=(6.8\pm 0.4(\text{stat})\pm 0.4(\text{syst}))\times {10}^{-6}$ which are in agreement with their respective current world averages. For the $CP$-violating parameters, we obtain ${\mathcal{A}}_{\omega K_S^0}=-0.36\pm 0.19(\text{stat})\pm 0.05(\text{syst}),{\mathcal{S}}_{\omega K_S^0}=+0.91\pm 0.32(\text{stat})\pm 0.05(\text{syst}),{\mathcal{A}}_{\omega K^{+}}=-0.03\pm 0.04(\text{stat})\pm 0.01(\text{syst}),$ where $\mathcal{A}$ and $\mathcal{S}$ represent the direct and mixing-induced $CP$ asymmetry, respectively. We find no evidence of $CP$ violation in the decay channel $B^{+}\to \omega K^{+}$; however, we obtain the first evidence of $CP$ violation in the $B^0\to \omega K_S^0$ decay channel at the level of 3.1 standard deviations.

Figure 1

Leading-order Feynman diagrams for $B\to \omega K$ decays. For $B^0\to \omega K_S^0$, (a) shows the loop (penguin), while (b) shows the tree diagram. For $B^{+}\to \omega K^{+}$, (c) and (d) are the corresponding diagrams. In the penguin diagrams, the subscript $x$ in $V_{xb}$ refers to the flavor of the intermediate-state up-type quark $(x=u,c,t)$.

Figure 2

Projections of the fit to the $B^0\to \omega K_S^0$ data enhanced in the signal region. Points with error bars represent the data, and the solid black curves or histograms represent the fit results. The signal enhancements, $-0.04\mathrm{GeV}<\mathrm{\Delta }E<0.03\mathrm{GeV}$, $M_{\text{bc}}>5.27\mathrm{GeV}/c^2$, ${\mathcal{F}}_{B\overline{B}/q\overline{q}}>1$, and $r>0.5$, except for the enhancement of the fit observable being plotted, are applied to each projection. (a), (b), (c), (d), and (e) show the $\mathrm{\Delta }E$, $M_{\text{bc}}$, ${\mathcal{F}}_{B\overline{B}/q\overline{q}}$, $M_{3\pi }$, and ${\mathcal{H}}_{3\pi }$ projections, respectively. Green hatched curves show the $B^0\to \omega K_S^0$ signal component, dashed red curves indicate the $q\overline{q}$ background, and blue dotted curves show the $B\overline{B}$ background component.

Figure 3

Projections of the fit to the $B^{+}\to \omega K^{+}$ data enhanced in the signal region. Points with error bars represent the data, and the solid black curves or histograms represent the fit results. The signal enhancements, $-0.04\mathrm{GeV}<\mathrm{\Delta }E<0.03\mathrm{GeV}$, $M_{\text{bc}}>5.27\mathrm{GeV}/c^2$, ${\mathcal{F}}_{B\overline{B}/q\overline{q}}>1$, and $r>0.5$, except for the enhancement of the fit observable being plotted, are applied to each projection. (a), (b), (c), (d), (e), and (f) show the $\mathrm{\Delta }E$, $M_{\text{bc}}$, ${\mathcal{F}}_{B\overline{B}/q\overline{q}}$, $M_{3\pi }$, ${\mathcal{H}}_{3\pi }$, and $\mathrm{\Delta }t$ projections, respectively. Green hatched curves show the $B^{+}\to \omega K^{+}$ signal component, dashed red curves indicate the $q\overline{q}$ background, and blue dotted curves show the $B\overline{B}$ background component.

Figure 4

Background subtracted time-dependent fit results for $B^0\to \omega K_S^0$. (a) shows the $\mathrm{\Delta }t$ distribution for each $B_{\text{Tag}}$ flavor $q$. The solid blue and dashed red curves represent the $\mathrm{\Delta }t$ distributions for $B^0$ and ${\overline{B}}^0$ tags, respectively. (b) shows the asymmetry of the plot above them, $(N_{B^0}-N_{{\overline{B}}^0})/(N_{B^0}+N_{{\overline{B}}^0})$, where $N_{B^0}$ ($N_{{\overline{B}}^0}$) is the measured signal yield of $B^0$ (${\overline{B}}^0$) events in each bin of $\mathrm{\Delta }t$.

Figure 5

Likelihood scan in the ${\mathcal{A}}_{\omega K_S^0}$-${\mathcal{S}}_{\omega K_S^0}$ plane including systematic uncertainties. The dashed circle represents the physical boundary of $CP$ violation. Starting from the red marker in the center that identifies the fit result, the concentric curves represent the contours from 1 to 5 standard deviations from the fit result.