[Paper Review] SU(3) - Flavor Symmetry in $B o VP$ Decays

Gil Paz|ArXiv.org|Jun 28, 2002

Quantum Chromodynamics and Particle Interactions2 references3 citations

TL;DR

This paper presents a systematic SU(3) flavor symmetry analysis of B→VP decays, identifying constraints on the CKM angle γ using tree-level and electroweak penguin amplitudes. It derives new constraints from B⁰→Kπ and B⁺→π⁰π⁺ modes, and proposes a novel method to measure γ via Bₛ⁰→ρπ and B⁰→K*±K∓ decays, extending prior SU(3)-based approaches beyond pseudoscalar-pseudoscalar modes.

ABSTRACT

In the framework of SU(3) symmetry, we present a general analysis of $B$ meson decays into two lighter uncharmed mesons (both pairs of pseudoscalar mesons and pairs of vector and pseudoscalar mesons). From the analysis we find constraints on $γ$ and discuss their validity. The most useful new constraint is obtained by considering the decay modes $B^{0} o Kπ$ and $B^{+} o π^{0}π^{+}$. In decays into pairs of vector and pseudeuscalar mesons, no constraints can be obtained using SU(3) symmetry alone and further assumptions are needed. Based on these assumptions, we obtain new (weaker) constraints using $B^{0} o ρK/B^{0} o K^{*}π$ and $B^{+} o ρπ$. We show that no other constraints can be obtained. We also suggest a method to measure $γ$ using $B^{0}_{s} o ρπ$ and $B^{0} o K^{*\pm}K^{\mp}$.

Motivation & Objective

• To systematically analyze SU(3) flavor symmetry constraints on the CKM angle γ in B→VP decays.
• To determine whether all possible SU(3)-based constraints on γ can be derived from B→VP decays without additional assumptions.
• To extend existing SU(3) methods beyond pseudoscalar-pseudoscalar decays to vector-pseudoscalar final states.
• To propose a new, viable method for measuring γ using Bₛ⁰→ρπ and B⁰→K*±K∓ decays.
• To clarify the role of electroweak penguin contributions and their relation to tree-level amplitudes in SU(3) symmetry.

Proposed method

• Reformulates the effective Hamiltonian using SU(3) symmetry and decomposes decay amplitudes into irreducible representations via Wigner-Eckart theorem.
• Applies the Neubert-Rosner method to B⁺→K⁺π⁰ and B⁺→K⁰π⁺ decays, relating electroweak penguin contributions to tree-level amplitudes.
• Uses the unitarity triangle condition V_ud V_ub* + V_cd V_cb* + V_td V_tb* = 0 to relate CKM matrix elements and extract γ constraints.
• Derives SU(3) decomposition tables (Tables 10–12) for B⁰→VP decays with ΔS=1 and ΔS=0, identifying amplitude components.
• Introduces a new measurement strategy for γ using Bₛ⁰→ρπ and B⁰→K*±K∓ decays, leveraging SU(3) symmetry and amplitude interference.
• Performs algebraic analysis of amplitude interference and CP-averaged branching ratios to extract γ constraints, including corrections from electroweak penguin contributions.

Experimental results

Research questions

• RQ1 Can all SU(3) symmetry-based constraints on γ be derived from B→VP decays without additional assumptions?
• RQ2 What are the new constraints on γ obtainable from B⁰→Kπ and B⁺→π⁰π⁺ decays using SU(3) symmetry?
• RQ3 Why are no constraints obtainable from B→VP decays using SU(3) symmetry alone, and what assumptions are required to derive weaker constraints?
• RQ4 Can a new, independent method for measuring γ be constructed using Bₛ⁰→ρπ and B⁰→K*±K∓ decays?
• RQ5 How do electroweak penguin contributions relate to tree-level amplitudes in SU(3) symmetry, and can this relation be used to constrain γ?

Key findings

• The decay modes B⁰→Kπ and B⁺→π⁰π⁺ provide a new, useful constraint on the CKM angle γ using SU(3) symmetry.
• For B→VP decays, no constraints on γ can be obtained using SU(3) symmetry alone; additional assumptions are required.
• With additional assumptions, weaker constraints on γ are derived using B⁰→ρK / B⁰→K*π and B⁺→ρπ decay modes.
• The paper identifies that no further constraints on γ can be obtained beyond those derived from the B⁰→Kπ and B⁺→π⁰π⁺ modes.
• A new method to measure γ is proposed using the decay modes Bₛ⁰→ρπ and B⁰→K*±K∓, which are sensitive to the γ phase through SU(3) amplitude interference.
• The electroweak penguin contribution is related to the tree-level amplitude via a universal factor ≈ 0.65, derived from Wilson coefficients and CKM matrix elements.