Testing QCD factorization with phase determinations in $B\to K\pi$,$K\rho$ and $ K^{*}\pi$ decays

TL;DR

This paper tests QCD factorization predictions by extracting decay amplitude phases from experimental data in B meson decays to light mesons, finding good agreement and indicating small final-state interaction phases.

Contribution

It introduces a method to determine decay amplitude phases in B decays using measured rates and QCDF predictions, providing a precise test of the factorization approach.

Findings

Extracted phases differ only slightly from QCDF predictions.

No evidence of large final-state interaction phases.

Supports the validity of QCDF in these decays.

Abstract

The success of QCD factorization(QCDF) in predicting branching ratios for charmless $B$ decays to light pseudoscalar and vector mesons and the small CP asymmetries measured at $BABAR$, Belle and LHCb show that the phase in these decays, as predicted by QCDF, are not large. For a precise test of QCDF one needs to extract from the measured decay rates, the phase of the decay amplitude which appears in the interference terms between the tree and penguin contribution. Since the tree amplitude is known at the leading order in $\Lambda_{\rm QCD}/m_{b}$ and is consistent with the measured tree-dominated decay rates, the QCDF value for the tree amplitude can be used with the measured decay rates to obtain the phases in $B\to K\pi$,$K\rho$, and $ K^{*}\pi$ decay rates. This is similar to the extraction of the final-state interaction phases in the interference term between $p\bar{p}\to J/\Psi\to e^{+}e^{-}$ and $p\bar{p}\to e^{+}e^{-} $ and in $J/\Psi\to 0^{-}0^{-}$ done previously. In this paper, we present a determination of the phase between the $I=3/2$ tree and $I=1/2$ penguin amplitudes in $B\to K\pi$,$K\rho$ , and $ K^{*}\pi$ decays using the measured decay rates and the QCDF $I=3/2$ tree amplitude obtained from the $I=2$ $B^{+}\to \pi^{+}\pi^{0},\rho^{0}\pi^{+}, \rho^{+}\pi^{0 tree-dominated decays and compare the result with the phase given by QCDF. It is remarkable that the phase extracted from experiments differs only slightly from the QCDF values. This shows that there is no large final-state interaction strong phase in $B\to K\pi$,$K\rho$, and $ K^{*}\pi$ decays.