Polarizations of two vector mesons in B decays

Abstract

Inspired by the small longitudinal polarizations (LPs) of $B\to K^{\ast }\varphi$ decays observed by BELLE and BABAR, we revise the theoretical uncertainties of perturbative QCD approach for determining hard scales of B decays, we find that the LPs of $B\to K^{\ast }\varphi$ could approach to 60% while the branching ratios (BRs) could be around $9\times 10^{-6}$. In addition, we also study the BRs and polarization fractions of $B\to \rho (\omega )\rho (\omega )$ and $B\to \rho (\omega )K^{\ast }$ decays. For those tree dominant and color-allowed processes in $B\to \rho (\omega )\rho (\omega )$ decays, we get that the BRs of $({\rho }^{+}{\rho }^{-},{\rho }^0{\rho }^{+},\omega {\rho }^{+})$ are $(23.06,11.99,14.78)\times 10^{-6}$ while their LPs are close to unity. Interestingly, due to significant tree contributions, we find that the BR(LP) of ${\rho }^{-}{K}^{\ast +}$ could be around $10.13\times 10^{-6}(60$; and due to the tree and electroweak penguin, the BR(LP) of $\omega K^{\ast +}$ could be around $5.67\times 10^{-6}(61$.

Comments: 14 pages, 1 figure, typos and references revised