CP asymmetries in charged meson decay to two pions

TL;DR

This paper analyzes CP asymmetries in charged meson decays to two pions, clarifying the isospin limit and estimating asymmetry sizes within the Standard Model.

Contribution

It provides a unified formalism for understanding CP asymmetries in charged meson decays and estimates their magnitudes in the Standard Model.

Findings

CP asymmetries vanish in the isospin limit.

Estimated asymmetries are approximately 0.003 for B+ decays.

Estimated asymmetries are around 10^-5 for D+ and 10^-6 for K+ decays.

Abstract

We study the CP asymmetries in $B^+$, $D^+$, and $K^+$ decays into $\pi^+\pi^0$. These asymmetries are commonly known to vanish in the isospin limit. We clarify what is meant by the term ``isospin limit" in this context. We provide a unified formalism to discuss these asymmetries, and develop an understanding of how various suppression factors distinguish between them qualitatively. We estimate the size of the asymmetries in the Standard Model: $A_{CP}(B^+\to\pi^+\pi^0)\sim 3\times10^{-3}$, $A_{CP}(D^+\to\pi^+\pi^0)\sim 10^{-5}$, and $A_{CP}(K^+\to\pi^+\pi^0)\sim 10^{-6}$