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

In this article, 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 ${\rm Y}\left(4S\right)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider. We obtain the branching fractions $B(B^0\to \omega K^0)=(4.5\pm 0.4(\text{stat})\pm 0.3(\text{syst}\left)\right)\times {10}^{-6},B(B^{+}\to \omega K^{+})=(6.8\pm 0.4(\text{stat})\pm 0.4(\text{syst}\left)\right)\times {10}^{-6}$ which are in agreement with their respective current world averages. For the $CP$-violating parameters, we obtain $A_{\omega K_S^0}=-0.36\pm 0.19\left(\text{stat}\right)\pm 0.05\left(\text{syst}\right),S_{\omega K_S^0}=+0.91\pm 0.32\left(\text{stat}\right)\pm 0.05\left(\text{syst}\right),A_{\omega K^{+}}=-0.03\pm 0.04\left(\text{stat}\right)\pm 0.01\left(\text{syst}\right),$ where $A$ and $S$ 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.