Tree and penguin amplitudes from B to pi pi, K pi, K bar{K}

TL;DR

This paper analyzes the relative sizes of tree and penguin amplitudes in B meson decays using experimental data and Regge phenomenology to estimate SU(3) breaking, concluding the true tree amplitude ratio is small.

Contribution

It introduces a method to extract the size and phase of penguin amplitudes from decay data using Regge-based SU(3) breaking estimates, providing a new way to determine the true tree amplitude ratio.

Findings

The C/T ratio of true tree amplitudes is approximately 0.2.

Regge phenomenology effectively estimates SU(3) breaking in hadronization.

The relative size and phase of penguin amplitudes can be unambiguously extracted from decay data.

Abstract

The question of the relative size of tree and penguin amplitudes is analyzed using the data on B to pi pi, B^+ to pi^+ K^0, and B^+ to K^+ \bar{K}^0 decays. Our discussion involves an estimate of SU(3) breaking in the final quark-pair-creating hadronization process. The estimate is based on Regge phenomenology, which many years ago proved very successful in the description of soft hadronic physics. Accepting the Regge prediction as solid, it is then shown that the relative size and phase of the two parts of the penguin amplitude can be unambiguously extracted from the data on the decays considered. This enables fixing the C/T ratio of `true' tree amplitudes, which - on the basis of the existing data - is shown to be small (of the order of 0.2).