Testing explanations of theB→ϕK*polarization puzzle

Abstract

B{yields}{phi}K* (b{yields}s) is three separate decays, one for each polarization of the final-state vector mesons (one longitudinal, two transverse). It is observed that the fraction of transverse decays, f{sub T}, and the fraction of longitudinal decays, f{sub L}, are roughly equal: f{sub T}/f{sub L}{approx_equal}1, in opposition to the naive expectation that f{sub T}<<f{sub L}. If one requires a single explanation of all polarization puzzles, two possibilities remain within the standard model: penguin annihilation and rescattering. In this paper we examine the predictions of these two explanations for f{sub T}/f{sub L} in b{yields}d decays. In B{yields}{rho}{rho} decays, only B{sub d}{sup 0}{yields}{rho}{sup 0}{rho}{sup 0} can possibly exhibit a large f{sub T}/f{sub L}. In B decays related by U-spin, we find two promising possibilities: (i) B{sup +}{yields}K*{sup 0}{rho}{sup +} (b{yields}s) and B{sup +}{yields}K*{sup 0}K*{sup +} (b{yields}d) and (ii) B{sub s}{yields}K*{sup 0}K*{sup 0} (b{yields}s) and B{sub d}{sup 0}{yields}K*{sup 0}K*{sup 0} (b{yields}d). The measurement of f{sub T}/f{sub L} in these pairs of decays will allow us to test penguin annihilation and rescattering. Finally, it is possible to distinguish penguin annihilation from rescattering by performing a time-dependent angular analysis of B{sub d}{sup 0}{yields}K*{sup 0}K*{sup 0}.