CP asymmetries in three-body B+- decays to charged pions and kaons

TL;DR

This paper analyzes CP asymmetries in three-body B+ decays involving pions and kaons, comparing experimental measurements with theoretical predictions based on U-spin symmetry, and explores the effects of resonant and non-resonant interactions on these asymmetries.

Contribution

It provides a detailed comparison of measured CP asymmetries with U-spin symmetry predictions and investigates the role of rescattering effects in three-body B+ decays.

Findings

Large CP asymmetries (~60%) observed in specific Dalitz plot regions.

U-spin symmetry predicts opposite sign asymmetries for related decay modes.

Rescattering effects may explain the observed asymmetry patterns.

Abstract

CP asymmetries have been measured recently by the LHCb collaboration in three-body $B^+$ decays to final states involving charged pions and kaons. Large asymmetries with opposite signs at a level of about 60% have been observed in $B^\pm\to \pi^\pm({\rm or} K^\pm)\pi^+\pi^-$ and $B^\pm \to \pi^\pm K^+K^-$ for restricted regions in the Dalitz plots involving $\pi^+\pi^-$ and $K^+K^-$ with low invariant mass. U-spin is shown to predict corresponding $\Delta S=0$ and $\Delta S=1$ asymmetries with opposite signs and inversely proportional to their branching ratios, in analogy with a successful relation predicted thirteen years ago between asymmetries in $B_s\to K^-\pi^+$ and $B^0 \to K^+ \pi^-$. We compare these predictions with the measured integrated asymmetries. Effects of specific resonant or non-resonant partial waves on enhanced asymmetries for low-pair-mass regions of the Dalitz plot are studied in $B^\pm \to \pi^\pm \pi^+\pi^-$. The closure of low-mass $\pi^+\pi^-$ and $K^+K^-$ channels involving only $\pi\pi \leftrightarrow K\bar K$ rescattering may explain by CPT approximately equal magnitudes and opposite signs measured in $B^\pm\to \pi^\pm\pi^+\pi^-$ and $B^\pm \to \pi^\pm K^+K^-$.