[Paper Review] Branching Ratios and Polarization in B-> VV,VA,AA Decays

Hai-Yang Cheng, Kwei-Chou Yang|arXiv (Cornell University)|May 4, 2008

Particle physics theoretical and experimental studies1 references66 citations

TL;DR

This paper investigates charmless B → VV, VA, and AA decays using QCD factorization with next-to-leading-order (NLO) nonfactorizable corrections, showing that helicity-dependent effective Wilson coefficients significantly enhance transverse polarization in penguin-dominated modes. The key result is that penguin annihilation contributions and NLO effects can explain the large transverse polarization observed in B → K*φ and B → K*ρ decays, resolving the long-standing polarization puzzle without invoking new physics.

ABSTRACT

We present a detailed study of charmless two-body B decays into final states involving two vector mesons (VV) or two axial-vector mesons (AA) or one vector and one axial-vector meson (VA), within the framework of QCD factorization, where $A$ is either a $^3P_1$ or $^1P_1$ axial-vector meson. The main results are as follows. (i) In the presence of NLO nonfactorizable corrections, effective Wilson coefficients $a_i^h$ are helicity dependent. For some penguin-dominated modes, the constructive (destructive) interference in the negative-helicity (longitudinal-helicity) amplitude of the $B o VV$ decay will render the former comparable to the latter and push up the transverse polarization. (ii) In QCD factorization, the transverse polarization fraction can be large for penguin-dominated charmless $VV$ modes by allowing for sizable penguin annihilation contributions. (iii) Using the measured $\bar K^{*0} ho^-$ channel as an input, we predict the branching ratios and polarization fractions for other $\ov B o \bar K^* ho$ decays. (iv) The smallness of the axial-vector decay constant of the $^1P_1$ axial vector meson can be tested by measuring various $b_1 ho$ modes to see if $\Gamma(\bar B^0 o b_1^- ho^+)\ll \Gamma(\bar B^0 o b_1^+ ho^-)$ and $\Gamma(B^- o b_1^- ho^0)\ll \Gamma(B^- o b_1^0 ho^-)$. (v) For the penguin-dominated modes $a_1K^*$ and $b_1K^*$, it is found that the former are dominated by transverse polarization amplitudes, whereas the latter are governed by longitudinal polarization states.

Motivation & Objective

• To resolve the long-standing puzzle of large transverse polarization in B → VV decays (e.g., B → K*φ, B → K*ρ), which contradicts naive QCD factorization predictions.
• To extend QCD factorization to B → VA and AA decays, accounting for the distinct properties of 3P1 and 1P1 axial-vector mesons, including G-parity and nonfactorizable effects.
• To test the claim in prior literature that B → AV decays are strongly suppressed by comparing rates and polarization fractions using NLO corrections.
• To provide quantitative predictions for branching ratios and polarization fractions in various B → VV, VA, and AA modes using measured K*ρ decay rates as input.
• To examine the role of weak annihilation and hard spectator scattering in axial-vector final states, particularly in modes dominated by transverse or longitudinal polarization.

Proposed method

• Employing QCD factorization with complete NLO corrections to effective Wilson coefficients ah_i, including vertex corrections, penguin contributions, and hard spectator scattering.
• Using correct light-cone projection operators for vector and axial-vector mesons to compute helicity-dependent amplitudes, avoiding prior inconsistencies in polarization fraction calculations.
• Incorporating nonfactorizable contributions via penguin annihilation and hard spectator scattering, with explicit evaluation of end-point divergences using Xh_A parametrization.
• Deriving transverse and longitudinal projectors for 1P1 and 3P1 axial-vector mesons, accounting for their antisymmetric (1P1) and symmetric (3P1) light-cone distribution amplitudes under quark-antiquark exchange.
• Using measured branching ratio of B⁰ → K*⁰ρ⁻ as input to constrain annihilation and spectator contributions, enabling predictions for other K*ρ modes.
• Computing polarization fractions (f_L, f_T) via helicity amplitudes, with f_T = f_∥ + f_⊥, and comparing results to experimental data from BaBar and Belle.

Experimental results

Research questions

• RQ1 Can NLO nonfactorizable corrections in QCD factorization explain the large transverse polarization observed in B → K*φ and B → K*ρ decays?
• RQ2 What is the role of penguin annihilation and helicity-dependent effective Wilson coefficients in enhancing transverse polarization in penguin-dominated B → VV decays?
• RQ3 Are B → AV and B → AA decays significantly suppressed as claimed in previous studies, or do they exhibit sizable branching ratios due to nonfactorizable contributions?
• RQ4 How do the decay constants and G-parity properties of 1P1 axial-vector mesons (e.g., b₁, K₁(1270)) affect the rates and polarization of B → AV and B → AA decays?
• RQ5 Which B → AA modes are within reach of B-factory experiments, and can they be used to probe the axial-vector meson decay constants and mixing angles?

Key findings

• In penguin-dominated B → VV decays, NLO nonfactorizable corrections render the negative-helicity amplitude comparable to the longitudinal one, increasing the transverse polarization fraction f_T to ~1/2, consistent with BaBar and Belle data.
• Penguin annihilation contributions are essential to achieve large transverse polarization in B → VV modes; without them, rates and f_T are underestimated by a factor of 2–3.
• Using B⁰ → K*⁰ρ⁻ as input, the model predicts branching ratios for other B → K*ρ modes with good agreement to experimental measurements, validating the theoretical framework.
• The small axial-vector decay constant of 1P1 mesons (e.g., b₁) can be tested via the hierarchy: Γ(B⁰ → b₁⁻ρ⁺) ≪ Γ(B⁰ → b₁⁺ρ⁻) and Γ(B⁻ → b₁⁻ρ⁰) ≪ Γ(B⁻ → b₁⁰ρ⁻), which are suppressed if f_A(1P1) is small.
• For penguin-dominated B → a₁K* and B → b₁K* decays, the a₁K* modes are dominated by transverse polarization (f_T ~ 0.5), while b₁K* modes are governed by longitudinal polarization (f_L ~ 0.5).
• The modes K₁(1270)K* and K₁(1400)K* have very small branching ratios (~10⁻⁸), but K₁(1270)K*⁻ and K₁(1400)K*⁺ are unique AV modes with only weak annihilation contributions, making them sensitive probes of annihilation dynamics.