Symmetry relations in charmless B->PPP decays

Abstract

Strangeness-changing decays of $B$ mesons to three-body final states of pions and kaons are studied, assuming that they are dominated by a $\Delta I=0$ penguin amplitude with flavor structure $\bar{b}\to \bar{s}$. Numerous isospin relations for $B\to K\pi \pi$ and for underlying quasi-two-body decays are compared successfully with experiment, in some cases resolving ambiguities in fitting resonance parameters. The only exception is a somewhat small branching ratio noted in $B^0\to K^{\ast 0}{\pi }^0$, interpreted in terms of destructive interference between a penguin amplitude and an enhanced electroweak penguin contribution. Relations for B decays into three kaons are derived in terms of final states involving $K_S$ or $K_L$, assuming that $\varphi K$-subtracted decay amplitudes are symmetric in $K$ and $\bar{K}$, as has been observed experimentally. Rates due to nonresonant backgrounds are studied using a simple model, which may reduce discrete ambiguities in Dalitz plot analyses.

Comments: 18 pages, 1 figure, text and references added, some measurements updated, version to be published in Physical Review D