Non Standard $η-η^{\prime}$ mixing and the Nonleptonic B and $Λ_b$ Decays to $η$ and $η^{\prime}$

Abstract

Radial mixing in the pseudoscalar $η-η^{\prime}$ systems can be generated from hyperfine interactions and annihilation terms. For the $η-η^{\prime}$ system we find the effects of radial mixing are appreciable and seriously affect the decay branching ratios for $B \to η(η^{\prime})K(K^*)$, mainly by modifying the $B \to η(η^{\prime})$ form factors. In particular, the effect of radial mixing in conjunction with the interference effects among penguin amplitudes can resolve puzzles in the $B \to η(η^{\prime}) K$ decays. The decay $Λ_b \to Λη(η^{\prime})$ on the other hand is dominated by a single amplitude so that the significant interference effects of B decays are absent here. Moreover, since no $Λ_b \to η(η^{\prime})$ form factors are involved here, the effect of radial mixing is essentially negligible. Hence, unlike the B system, we do not predict a large enhancement of $Λ_b \to Λη^{\prime}$ relative to $Λ_b \to Λη$.