Charmless B Decays to Final States with Radially Excited Vector Mesons

We consider the weak decays of a B meson to final states that contain a S-wave radially excited vector meson. We consider vector-pseudoscalar final states and calculate ratios of the type $B \to \rho^{\prime} \pi/B \to \rho \pi$, $B \to \omega^{\prime} \pi/B \to \omega \pi$ and $B \to \phi^{\prime} \pi/B \to \phi \pi$ where $\rho^{\prime}$, $\omega^{\prime}$ and $\phi^{\prime}$ are higher $\rho$, $\omega$ and $\phi$ S-wave radial excitations. 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 system generated from hyperfine interaction and the annihilation term.