[Paper Review] Measurement of alpha/phi2 in Bo --> pi pi, rho pi and rho rho

J. Dalseno|arXiv (Cornell University)|Jan 10, 2011

Particle physics theoretical and experimental studies3 references3 citations

TL;DR

This paper presents updated measurements of the CKM angle α (φ₂) from B⁰ → ππ, ρπ, and ρρ decays using data from the BaBar and Belle experiments at the Υ(4S) resonance. By analyzing time-dependent CP asymmetries and employing isospin symmetry to suppress penguin pollution, the experiments constrain φ₂ with improved precision, yielding consistent results across final states and supporting the Standard Model prediction.

ABSTRACT

We present a summary of the measurements of the CKM angle, alpha (phi2), performed by the BaBar and Belle experiments which collect BBbar pairs at the Y(4S) resonance produced in asymmetric e+ e- collisions. We discuss the measurements of the branching fractions and CP asymmetries in the B --> pi pi, rho pi and rho rho final states that lead to constraints on alpha (phi2).

Motivation & Objective

• To precisely determine the CKM angle α (φ₂) using B⁰ → ππ, ρπ, and ρρ decay modes.
• To test the Standard Model's description of CP violation via measurements of direct and mixing-induced CP asymmetries.
• To reduce theoretical uncertainty from penguin pollution using isospin symmetry in the B → ππ and B → ρρ systems.
• To provide a consistent constraint on φ₂ across multiple decay modes, improving global unitarity triangle fits.

Proposed method

• Time-dependent CP asymmetry analysis using the decay sequence Υ(4S) → B⁰B̄⁰ → fCP fTag, with ∆t = tCP − tTag.
• Measurement of ACP (direct CP violation) and SCP (mixing-induced CP violation) from the time-dependent decay rate: P(∆t, q) = e^−|∆t|/τB⁰ / (4τB⁰) × [1 + q(ACP cos ∆md∆t + SCP sin ∆md∆t)].
• Use of isospin symmetry to relate amplitudes in B → ππ and B → ρρ modes, enabling extraction of φ₂ despite penguin contributions.
• Amplitude analysis on Dalitz plots for B⁰ → (ρπ)⁰, including strong phase variations across the plot to resolve interference effects.
• Combination of data from BaBar (467 million BB pairs) and Belle (535 million BB pairs) to improve statistical precision.
• Application of isospin triangle relations: A+0 = 1/√2 A+− + A00 and A−0 = 1/√2 A+− + A00, to determine ∆φ₂ and resolve φ₂ ambiguity.

Experimental results

Research questions

• RQ1 What is the current experimental constraint on the CKM angle α (φ₂) from B⁰ → ππ, ρπ, and ρρ decays?
• RQ2 To what extent do direct and mixing-induced CP asymmetries in these decays deviate from Standard Model expectations?
• RQ3 How effectively can isospin symmetry be used to disentangle penguin contributions and extract φ₂?
• RQ4 What is the impact of the B⁰ → ρ⁰ρ⁰ mode, despite its low branching fraction, on the global φ₂ constraint?
• RQ5 How do the results from BaBar and Belle compare across different decay modes, and what is the combined world average for φ₂?

Key findings

• BaBar measures ACP = +0.25 ± 0.08 ± 0.02 and SCP = −0.68 ± 0.10 ± 0.03 in B⁰ → π+π−, indicating significant CP violation at 6.3σ significance.
• Belle measures ACP = +0.55 ± 0.08 ± 0.05 and SCP = −0.61 ± 0.10 ± 0.04 in B⁰ → π+π−, showing 5.5σ evidence for CP violation.
• For B⁰ → ρ+ρ−, BaBar finds ACP = 0.01 ± 0.15 ± 0.06 and SCP = −0.17 ± 0.20+0.05−0.06, while Belle reports ACP = +0.16 ± 0.21 ± 0.07 and SCP = +0.19 ± 0.30 ± 0.07.
• BaBar determines φ₂ = (92.4+6.0−6.5)° from B → ρρ, while Belle finds φ₂ = (91.7 ± 14.9)°, with both consistent within uncertainties.
• In B⁰ → (ρπ)⁰, BaBar obtains φ₂ = (87+4.5−13)°, and Belle constrains 68° < φ₂ < 95° at 68.3% CL, showing good agreement.
• The world average for φ₂ from CKMfitter and Ufitter is φ₂ = (89.0+4.4−4.2)° and φ₂ = (91.4 ± 6.1)°, respectively, indicating consistency across experiments and modes.