Study of $B^0 \to \eta K^+ \pi^-$ and $\eta \pi^+ \pi^-$

We report results of studies of inclusive $B \to \eta K^+ \pi^-$ and $B \to \eta \pi^+ \pi^-$ decays. Charged conjugates are implied throughout this paper. These are obtained from a data sample containing 386 million $B\bar{B}$ pairs, collected at the $\Upsilon(4S)$ resonance, with the Belle detector at the KEKB asymmetric energy $e^+ e^-$ collider. The branching fraction of inclusive $B^0 \to \eta K^+\pi^-$ and $B^0 \to \eta \pi^+\pi^-$ are measured to be $\mathcal B$($B^0 \to \eta K^+ \pi^-$)= $(31.7\pm1.9 ^{+2.2}_{-2.6})\times 10^{-6}$ and $\mathcal B$($B^0 \to \eta \pi^+ \pi^-$)=$(6.2^{+1.8 + 0.8}_{-1.6 - 0.6})\times 10^{-6}$, where the first error is statistical and the second systematic. The decays $B^0\to a_0^- X^+$, where $X^+$= $K^+$, $\pi^+$ were searched for and no significant signals found. Upper limits of $\mathcal B$($B^0 \to a_0^- K^+$)$<1.6 \times 10^{-6}$ and $\mathcal B$($B^0 \to a_0^- \pi^+$)$< 2.8 \times 10^{-6}$ at 90% C.L. are obtained. Here the notation $B(B^0 \to a_0^- X^+)$ indicates the product of branching fractions for $B^0 \to a_0^- X^+$ and $a_0^- \to \eta \pi^-$.