[Paper Review] Status of the B -> pi K puzzle and its relation to B_s -> phi pi and B_s -> phi rho decays

Lars Hofer, Leonardo Vernazza|arXiv (Cornell University)|Dec 19, 2012

Particle physics theoretical and experimental studies3 references3 citations

TL;DR

This paper proposes that the long-standing B → πK puzzle—discrepancies between measured CP asymmetries and Standard Model predictions—may stem from new physics (NP) in electroweak penguin amplitudes. If such NP exists, it could enhance the branching ratios of Bs → φπ⁰ and Bs → φρ⁰ decays by up to a factor of 5 (model-independent) or 3 (model-dependent), offering a clean probe to test NP beyond the B → πK system.

ABSTRACT

Some discrepancies between theory and experiment in the B -> pi K decays suggest the possibility of a new physics contribution with the structure of an electroweak penguin amplitude. If such a scenario is realised in nature, the branching ratios of the decays B_s -> phi pi and B_s -> phi rho can be enhanced by about one order of magnitude. We review and update the current status of the B -> pi K puzzle and its implications for the decays B_s -> phi pi and B_s -> phi rho.

Motivation & Objective

• To assess whether unresolved discrepancies in B → πK decays suggest new physics beyond the Standard Model.
• To explore whether isospin-violating decays Bs → φπ⁰ and Bs → φρ⁰ can serve as sensitive probes for electroweak penguin-type new physics.
• To update constraints on NP contributions using latest experimental and theoretical inputs, particularly from B → ρK* decays and Bs-Bs mixing.
• To distinguish between different NP scenarios, especially those with opposite-parity contributions, using the helicity structure of Bs → φπ⁰ and φρ⁰ decays.
• To evaluate the viability of NP models (e.g., modified Z⁰ penguin, U(1)′, MSSM) in light of constraints from semileptonic decays and Bs-Bs mixing.

Proposed method

• Uses QCD factorisation (QCDF) to compute hadronic matrix elements for B → πK and Bs → φM decays.
• Introduces a model-independent NP amplitude with new weak phase δ, structured as an electroweak penguin, to modify the SM amplitude.
• Applies topological factorisation to express decay amplitudes in terms of colour-suppressed tree (rC), EW penguin (rEW), and NP contributions (˜rEW, ˜rC, ˜rA).
• Derives the observable ∆ACP = ACP(B⁻→π⁰K⁻) − ACP(B⁰→π⁺K⁻) as a key probe sensitive to imaginary parts of NP-modified amplitudes.
• Performs global fits using constraints from B → ρK* decays, semileptonic B → Xsℓ⁺ℓ⁻, radiative B → Xsγ, and Bs-Bs mixing to limit NP parameter space.
• Uses helicity structure differences (PV/VV vs. PP) to reduce non-perturbative QCD uncertainties and improve sensitivity to NP.

Experimental results

Research questions

• RQ1 Can the observed discrepancy in the direct CP asymmetry difference ∆ACP in B → πK decays be explained by a new physics contribution to electroweak penguin amplitudes?
• RQ2 To what extent can the branching ratios of Bs → φπ⁰ and Bs → φρ⁰ be enhanced if such NP exists, and can this enhancement be experimentally detected?
• RQ3 How do constraints from semileptonic decays and Bs-Bs mixing affect the allowed parameter space for NP in the EW penguin sector?
• RQ4 Can Bs → φπ⁰ and Bs → φρ⁰ decays distinguish between NP scenarios with different weak phases and parity structures, especially when B → πK data alone cannot?
• RQ5 What is the maximum possible enhancement of Bs → φπ⁰ and Bs → φρ⁰ branching ratios under model-independent and model-dependent analyses?

Key findings

• The model-independent analysis shows that Bs → φπ⁰ and Bs → φρ⁰ branching ratios can be enhanced by up to a factor of 5 compared to the SM, depending on constraints from other hadronic decays.
• The model-dependent analysis, incorporating constraints from semileptonic B → Xsℓ⁺ℓ⁻ and updated Bs-Bs mixing data, reduces the maximum possible enhancement to a factor of 3.
• The SM point is excluded at the 2σ level due to the ∆ACP measurement, supporting the existence of new physics with a non-zero imaginary part in the NP-modified electroweak penguin amplitude.
• The branching ratio enhancement is most significant in the isospin-violating decays Bs → φπ⁰ and Bs → φρ⁰, which are dominated by EW penguin amplitudes and less affected by QCD penguin interference.
• The helicity structure of Bs → φπ⁰ and Bs → φρ⁰ (PV and VV final states) reduces non-perturbative uncertainties compared to B → πK (PP final states), making them more reliable probes.
• In the modified Z⁰-penguin model with right-handed couplings, the allowed enhancement region for Bs → φπ⁰ and φρ⁰ is constrained to a factor of 3 or less, consistent with the global fit results.