The Riddle of Polarization in $B \to VV$ Transitions

Abstract

Measurements of polarization fractions in $B \to VV$ transitions, with $V$ a light vector meson, show that the longitudinal amplitude dominates in $B^0 \to \rho^+ \rho^-$, $B^+ \to \rho^+ \rho^0$, and $B^+ \to \rho^0 K^{*+}$ decays and not in the penguin induced decays $B^0 \to \phi K^{*0}$, $B^+ \to \phi K^{*+}$. We study the effect of rescattering mediated by charmed resonances, finding that in $B \to \phi K^*$ it can be responsible of the suppression of the longitudinal amplitude. For the decay $B \to \rho K^*$ we find that the longitudinal fraction cannot be too large without invoking new effects.