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Evidence for Direct<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>C</mml:mi><mml:mi>P</mml:mi></mml:math>Violation in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>B</mml:mi><mml:mo>±</mml:mo></mml:msup><mml:mo>→</mml:mo><mml:mi>η</mml:mi><mml:msup><mml:mi>h</mml:mi><mml:mo>±</mml:mo></mml:msup></mml:math>and Observation of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>B…
We report measurements of the branching fractions and $CP$ asymmetries for ${B}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\rightarrow}\ensuremath{\eta}{h}^{\ifmmode\pm\else\textpm\fi{}}$ ($h=K$ or $\ensuremath{\pi}$) and the observation of the decay ${B}^{0}\ensuremath{\rightarrow}\ensuremath{\eta}{K}^{0}$ from the final data sample of $772\ifmmode\times\else\texttimes\fi{}{10}^{6}\text{ }\text{ }B\overline{B}$ pairs collected with the Belle detector at the KEKB asymmetric-energy ${e}^{+}{e}^{\ensuremath{-}}$ collider. The measured branching fractions are $\mathcal{B}({B}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\rightarrow}\ensuremath{\eta}{K}^{\ifmmode\pm\else\textpm\fi{}})=(2.12\ifmmode\pm\else\textpm\fi{}0.23\ifmmode\pm\else\textpm\fi{}0.11)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$, $\mathcal{B}({B}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\rightarrow}\ensuremath{\eta}{\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}})=(4.07\ifmmode\pm\else\textpm\fi{}0.26\ifmmode\pm\else\textpm\fi{}0.21)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$, …