[Paper Review] Rescattering effects in charmless B_{u,d,s} to P P decays

Chun-Khiang Chua|arXiv (Cornell University)|Dec 27, 2007

Quantum Chromodynamics and Particle Interactions3 citations

TL;DR

This paper investigates final-state interactions (FSI) in charmless B→PP decays using a factorization-based FSI approach with both short- and long-distance contributions, constrained by flavor SU(3) symmetry. It successfully explains the Kπ CP violation puzzle by showing that residual rescattering lifts the degeneracy between A(B⁰→K⁻π⁺) and A(B⁻→K⁻π⁰), while generating sizable color-suppressed amplitudes via exchange rescattering, predicting enhanced B_s→η'η' branching ratios and small time-dependent CP asymmetries in B_s→PP modes.

ABSTRACT

We study the final-state interaction (FSI) effects in charmless B_{u,d,s} to PP decays. We consider a FSI approach with both short- and long-distance contributions, where the former are from in-elastic channels and are contained in factorization amplitudes, while the latter are from the residual rescattering among PP states. Flavor SU(3) symmetry is used to constrain the residual rescattering S-matrix. We fit to all available data on the CP-averaged decay rates and CP asymmetries, and make predictions on unmeasured ones. Our main results are as follows: (i) Results are in agreement with data in the presence of FSI. (ii) For B decays, the pi^+pi^- and pi^0pi^0 rates are suppressed and enhanced respectively by FSI. (iii) The FSI has a large impact on direct CP asymmetries of many modes. (iv) The deviation (Delta A) between A(B{bar}^0 to K^-pi^+) and A(B^-to K^-π^0) can be understood in the FSI approach. (v) Sizable and complex color-suppressed tree amplitudes, which are crucial for the large π^0π^0 rate and Delta A, are generated through exchange rescattering. The correlation of the ratio B(pi^0pi^0)/B(pi^+pi^-) and Delta A is studied. (vi) The B^- to pi^-pi^0 direct CP violation is very small and is not affected by FSI. (vii) Several B_s decay rates are enhanced. In particular, the eta'eta' branching ratio is enhanced to the level of 1.0X10^{-4}, which can be checked experimentally. (viii) Time-dependent CP asymmetries S in B_{d,s} decays are studied. CP asymmetries in these modes will be useful to test the SM.

Motivation & Objective

• To resolve the long-standing Kπ CP violation puzzle, where experimental A(B⁻→K⁻π⁰) is positive while A(B⁰→K⁻π⁺) is negative and large in magnitude.
• To understand the unexpectedly large branching ratio of B⁰→π⁰π⁰, which is not explained by standard factorization models.
• To predict unmeasured branching ratios and CP asymmetries in charmless B_u,d,s→PP decays, especially for B_s modes.
• To examine the role of final-state interactions in generating strong phases and modifying direct and time-dependent CP asymmetries.
• To test the Standard Model by predicting small time-dependent CP asymmetries in B_s→PP decays, which are sensitive to new physics.

Proposed method

• Uses a master formula for FSI: A^{FSI}_i = Σ_k S^{1/2}_{ik} A^0_k, where S is the S-matrix for residual rescattering among PP states.
• Applies flavor SU(3) symmetry to constrain the S-matrix elements, reducing the number of free parameters.
• Separates FSI contributions into short-distance (inelastic channels in factorization amplitudes) and long-distance (residual rescattering among PP states).
• Fits the model to all available CP-averaged branching ratios and direct CP asymmetries from experiment.
• Uses unitarity and time-reversal invariance to derive the S-matrix structure, ensuring consistency with strong interaction dynamics.
• Performs a U(3) symmetry analysis to derive constraints on rescattering parameters, leading to two distinct solutions: annihilation-type and exchange-type.

Experimental results

Research questions

• RQ1 Can final-state interactions explain the observed large direct CP asymmetry in B⁰→K⁻π⁺ and the opposite-sign asymmetry in B⁻→K⁻π⁰, resolving the Kπ puzzle?
• RQ2 What is the origin of the large B⁰→π⁰π⁰ branching ratio, which exceeds standard factorization predictions?
• RQ3 How do final-state interactions affect the direct CP asymmetry ΔA(Kπ) between B⁰→K⁻π⁺ and B⁻→K⁻π⁰ decays?
• RQ4 What are the predicted branching ratios and CP asymmetries for unmeasured B_s→PP decays, especially B_s→η'η'?
• RQ5 Are time-dependent CP asymmetries in B_s→PP modes small in the Standard Model, as predicted by this FSI model?

Key findings

• The model successfully reproduces all measured CP-averaged branching ratios and direct CP asymmetries, confirming the importance of FSI.
• Final-state interactions suppress the B⁰→π⁺π⁻ rate and enhance the B⁰→π⁰π⁰ rate, explaining the large observed π⁰π⁰ branching ratio.
• The deviation ΔA = A(B⁻→K⁻π⁰) − A(B⁰→K⁻π⁺) is explained by the sensitivity of A(B⁻→K⁻π⁰) to residual rescattering, lifting the degeneracy predicted by naive factorization.
• Sizable and complex color-suppressed tree amplitudes arise from exchange rescattering, which are crucial for explaining the large π⁰π⁰ rate and ΔA.
• The B⁻→π⁻π⁰ direct CP asymmetry is predicted to be very small and largely unaffected by FSI, consistent with experimental data.
• The B_s→η'η' branching ratio is enhanced to 1.0×10⁻⁴, a testable prediction for LHCb and future B factories.
• Time-dependent CP asymmetries in B_s→PP modes are small: |S| ≤ 0.06 for B_s⁰→ηη, ηη', and η'η', with S(B_s⁰→K_Sη') ≤ 1%, making it a clean probe for new physics.