Testing Explanations of the $B\to\phi K^*$ Polarization Puzzle

TL;DR

This paper investigates polarization puzzles in B meson decays, testing explanations like penguin annihilation and rescattering through predictions for specific decay modes and proposing measurements to distinguish these mechanisms.

Contribution

It provides theoretical predictions for polarization fractions in related B decays to test penguin annihilation and rescattering explanations within the Standard Model.

Findings

Predicted large polarization fractions in specific decay modes.

Identified decay pairs suitable for testing polarization mechanisms.

Suggested time-dependent angular analysis to distinguish explanations.

Abstract

$B\to\phi K^*$ ($\btos$) 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, $\fT$, and the fraction of longitudinal decays, $\fL$, are roughly equal: $\fTfL \simeq 1$, in opposition to the naive expectation that $\fT \ll \fL$. 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 $\fTfL$ in $\btod$ decays. In $B \to \rho\rho$ decays, only $\bd \to \rho^0\rho^0$ can possibly exhibit a large $\fTfL$. In B decays related by U-spin, we find two promising possibilities: (i) $B^+ \to K^{*0} \rho^+$ ($\btos$) and $B^+ \to \Kbar^{*0} K^{*+}$ ($\btod$) and (ii) $\bs \to K^{*0} \Kbar^{*0}$ ($\btos$) and $\bd \to \Kbar^{*0} K^{*0}$ ($\btod$). The measurement of $\fTfL$ 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 $\bd \to \Kbar^{*0} K^{*0}$.