[Paper Review] Theoretical status of the B --> pi K decays

Satoshi Mishima|arXiv (Cornell University)|Jan 7, 2011

Particle physics theoretical and experimental studies2 references3 citations

TL;DR

This paper reviews the theoretical status of B → πK decays, focusing on discrepancies between Standard Model predictions and experimental data, particularly in CP asymmetries. It examines QCD factorization and perturbative QCD approaches, identifying Glauber divergences in PQCD as a key source of strong phases that can resolve the πK and ππ puzzles simultaneously when the soft factor Se ≈ −π/2, leading to enhanced color-suppressed tree amplitudes and improved agreement with data.

ABSTRACT

We review the theoretical status of the B --> pi K decays, focusing on recent developments in the QCD factorization and perturbative QCD approaches as well as on the Standard-Model correlation between the mixing-induced and direct CP asymmetries of the B^0 --> pi^0 K^0 mode.

Motivation & Objective

• Address the persistent discrepancy between Standard Model predictions and experimental data in B→πK decays, particularly in direct CP asymmetries.
• Investigate the role of subleading corrections in QCD factorization and perturbative QCD approaches to explain the enhanced color-suppressed tree amplitude C′.
• Resolve the simultaneous πK and ππ decay puzzles by identifying nonperturbative Glauber dynamics as a source of large strong phases.
• Test the Standard Model using sum rules and isospin relations involving CP asymmetries in B0→π0K0 decays.
• Provide a phenomenological framework for future precision tests at super B factories.

Proposed method

• Analyzes B→πK decays using topological amplitude decomposition into T′, C′, P′, and P′_ew components with CKM phase φ3.
• Applies QCD factorization (QCDF) and perturbative QCD (PQCD) frameworks to compute power and higher-order corrections.
• Identifies uncanceled Glauber divergences in spectator-scattering amplitudes in PQCD, factorized via Wilson lines and soft factors depending on transverse separation b.
• Introduces the soft factor eiSe(b) defined through Wilson lines, with Se ≈ −π/2 yielding constructive interference and enhanced C′/T′.
• Uses isospin symmetry to relate I=3/2 amplitude A3/2 to B(π±π0), enabling correlation plots between ACP(π0KS) and Sπ0KS.
• Employs a model-independent sum rule to test the SM without assuming factorization, using measured branching ratios and lifetimes.

Experimental results

Research questions

• RQ1 Can the observed large direct CP asymmetry in B0→π0K0 relative to B0→π∓K± be explained within the Standard Model?
• RQ2 What is the origin of the enhanced color-suppressed tree amplitude C′, which explains the large B(π0π0) branching ratio?
• RQ3 Do Glauber divergences in PQCD provide a viable source of large strong phases to resolve the πK and ππ puzzles simultaneously?
• RQ4 How do subleading 1/mb corrections in QCDF affect the stability of CP asymmetry predictions?
• RQ5 Can sum rules and isospin relations provide robust, model-independent tests of the SM in B→πK decays?

Key findings

• A soft factor Se ≈ −π/2 in PQCD enhances the color-suppressed tree amplitude C′/T′ to ∼0.5 e−2.2i, resolving both the πK and ππ decay puzzles simultaneously.
• The predicted B(π0π0) increases to ∼2.5×10−6 under Se ≈ −π/2, consistent with data (1.55±0.19×10−6), while B(ρ0ρ0) remains consistent with data.
• ACP(π∓K±) and ACP(π0K±) differ significantly under Se ≈ −π/2, with ACP(π∓K±) ≈ −10% and ACP(π0K±) ≈ +5%, matching experimental data.
• The mixing-induced CP asymmetry Sπ0KS is reduced under Se ≈ −π/2, aligning better with data and reducing tension in the S–ACP correlation.
• The sum rule predicts ACP(π0K0) = −0.15 ± 0.04, while data show ACP(π0K0) = −0.01 ± 0.10, indicating a tension that may signal new physics or non-factorizable effects.
• The isospin-based correlation between ACP(π0KS) and Sπ0KS shows tension with current data, suggesting the need for improved measurements at super B factories.