On Charmless $B\to K_h\eta^{(')}$ Decays with $K_h=K,K^*,K_0^*(1430),K_2^*(1430)$

Understand

We study the charmless decays $B\to K_h\eta$ and $B\to K_h\eta'$ within the framework of QCD factorization (QCDF) for $K_h= K,K^*,K_0^*(1430)$ and naive factorization for $K_h=K_2^*(1430)$.

• There are three distinct types of penguin contributions: (i) $b\to sq\bar q\to s\eta_{q}$, (ii) $b\to ss\bar s\to s\eta_s$, and (iii) $b\to s q\bar q\to q \bar K_h$, where $\eta_q=(u\bar u+d\bar d)/\sqrt{2}$ and $\eta_s=s\bar s$.
• $B\to K^{(*)}\eta^{(')}$ decays are dominated by type-II and type-III penguin contributions.
• The interference, constructive for $K\eta'$ and $K^*\eta$ and destructive for $K\eta$ and $K^*\eta'$, between type-II and type-III diagrams explains the pattern of $\Gamma(B\to K\eta')\gg\Gamma(B\to K\eta)$ and $\Gamma(B\to K^*\eta')\ll\Gamma(B\to K^*\eta)$.