B -> V_L V_L Decays at Next-to-Leading Order in QCD

Abstract

We compute the amplitudes for the two-body decay of $B$ mesons into longitudinally polarized light vector mesons at next-to-leading order in QCD. We give the explicit expressions in QCD factorization for all 34 transitions of a heavy-light $B$ meson into a pair of longitudinal vector mesons $\rho$, $\omega$, $\phi$, $K^*$ within the Standard Model. Decay rates and CP asymmetries are discussed in detail and compared with available data. Exploiting the fact that QCD penguins are systematically smaller for vector mesons in comparison to pseudoscalars in the final state, we investigate several methods to achieve high-precision determinations of CKM parameters and New Physics tests. We propose a method to use V-spin symmetry and data on $\bar B_d\to\bar K^{*0}_L K^{*0}_L$ to constrain the penguin contribution in $\bar B_d\to\rho^+_L\rho^-_L$. CP violation in the latter decay together with a measurement of $\sin 2\beta$ determines the unitarity triangle with high accuracy. We show that CP violation in $\bar B_d\to\rho^+_L\rho^-_L$ and $\bar B_d\to\psi K_S$ alone implies $|V_{ub}|=(3.54\pm 0.17)\cdot 10^{-3}$, presently the most accurate determination of this quantity.