Weak decays to final states with Radial Excitation Admixtures

We consider the weak decays of a B meson to final states that are mixtures of S-wave radially excited components. We consider non leptonic decays of the type $B \to \rho' \pi/B \to \rho \pi$, $B \to \omega' \pi/B \to \omega \pi$ and $B \to \phi' \pi/B \to \phi \pi$ where $\rho'$, $\omega'$ and $\phi'$ are higher $\rho$, $\omega$ and $\phi$ resonances. We find such decays to have larger or similar branching ratios compared to decays where the final state $\rho$, $\omega$ and $\phi$ are in the ground state. We also study the effect of radial mixing in the vector and the pseudoscalar systems generated from hyperfine interaction and the annihilation term. We find the effects of radial mixing to be small and generally negligible for all practical purposes in the vector system. However, in the $\eta-\eta^{\prime}$ system the effects of radial mixing are appreciable and seriously affect decay branching ratios for $B \to \eta(\eta')K(K^*)$. In particular we find that nonstandard $\eta(\eta')$ mixing can resolve the puzzles in $B \to \eta(\eta')K$ decays.