Flavor SU(3) Topological Diagram and Irreducible Representation Amplitudes for Heavy Meson Charmless Hadronic Decays: Mismatch and Equivalence

TL;DR

This paper compares two SU(3) analysis methods for heavy meson decays, identifies mismatches in previous work, introduces new amplitudes, and shows these impact CP asymmetries, challenging previous assumptions of zero CP violation.

Contribution

It reveals inconsistencies between IRA and TDA methods, introduces missing amplitudes, and provides a unified framework for analyzing heavy meson decays.

Findings

Previous analyses had overlooked SU(3) independent amplitudes in TDA.

Including new amplitudes leads to consistent results between IRA and TDA.

Direct CP asymmetries can be significantly affected, implying CP violation is generally non-zero.

Abstract

Flavor SU(3) analysis of heavy meson ($B$ and $D$) hadronic charmless decays can be formulated in two different ways. One is to construct the SU(3) irreducible representation amplitude (IRA) by decomposing effective Hamiltonian according to the SU(3) transformation properties. The other is to use the topological diagrams (TDA). These two methods should give equivalent physical results in the SU(3) limit. Using $B \to PP$ decays as an example, we point out that previous analyses in the literature using these two methods do not match consistently in several ways, in particular a few SU(3) independent amplitudes have been overlooked in the TDA approach. Taking these new amplitudes into account, we find a consistent description in both schemes. These new amplitudes can affect direct CP asymmetries in some channels significantly. A consequence is that for any charmless hadronic decay of heavy meson, the direct CP symmetry cannot be identically zero.