Non Standard $\eta -{\eta }^{\prime }$ mixing and the Nonleptonic B and ${\Lambda }_b$ Decays to $\eta$ and ${\eta }^{\prime }$

Abstract

Radial mixing in the pseudoscalar $\eta -{\eta }^{\prime }$ systems can be generated from hyperfine interactions and annihilation terms. For the $\eta -{\eta }^{\prime }$ system we find the effects of radial mixing are appreciable and seriously affect the decay branching ratios for $B\to \eta ({\eta }^{\prime })K(K^{\ast })$, mainly by modifying the $B\to \eta ({\eta }^{\prime })$ form factors. In particular, the effect of radial mixing in conjunction with the interference effects among penguin amplitudes can resolve puzzles in the $B\to \eta ({\eta }^{\prime })K$ decays. The decay ${\Lambda }_b\to \Lambda \eta ({\eta }^{\prime })$ 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 ${\Lambda }_b\to \eta ({\eta }^{\prime })$ 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 ${\Lambda }_b\to \Lambda {\eta }^{\prime }$ relative to ${\Lambda }_b\to \Lambda \eta$.

Comments: Typos corrected, Minor addition of text, Latex, 16 pages, one fig