[Paper Review] Phenomenology of B{yields}{pi}{pi}, {pi}K decays at O({alpha}{sub s}{sup 2}{beta}{sub 0}) in QCD factorization

Craig N. Burrell, Alexander R. Williamson|arXiv (Cornell University)|Jun 1, 2006

Particle physics theoretical and experimental studies61 references5 citations

TL;DR

This paper computes O(α²ₛβ₀) perturbative QCD corrections to B → ππ and B → πK decay matrix elements within the QCD factorization framework, including chirally enhanced power corrections. It finds that these higher-order corrections are often comparable in magnitude to O(αₛ) terms, leading to significant renormalization scale uncertainties and poor constraints on nonperturbative parameters, which strongly affect direct CP asymmetries in B⁰ → π⁺π⁻.

ABSTRACT

We study O({alpha}{sub s}{sup 2}{beta}{sub 0}) perturbative corrections to matrix elements entering two-body exclusive decays of the form B{yields}{pi}{pi}, {pi}K in the QCD factorization formalism, including chirally enhanced power corrections, and discuss the effect of these corrections on direct CP asymmetries, which receive their first contribution at O({alpha}{sub s}). We find that the O({alpha}{sub s}{sup 2}{beta}{sub 0}) corrections are often as large as the O({alpha}{sub s}) corrections. We find large uncertainties due to renormalization scale dependence as well as poor knowledge of the nonperturbative parameters. We assess the effect of the perturbative corrections on the direct CP violation parameters of B{sup 0}{yields}{pi}{sup +}{pi}{sup -}.

Motivation & Objective

• To compute next-to-leading-order perturbative QCD corrections at O(α²ₛβ₀) for exclusive two-body B decays into ππ and πK final states.
• To assess the impact of these corrections on direct CP asymmetries, which first arise at O(αₛ).
• To include chirally enhanced power corrections within the QCD factorization formalism.
• To evaluate the sensitivity of CP asymmetry predictions to renormalization scale dependence and nonperturbative parameters.

Proposed method

• Employing the QCD factorization approach to calculate matrix elements for B → ππ and B → πK decays at O(α²ₛβ₀).
• Including chirally enhanced power corrections that arise from the structure of the effective Hamiltonian and quark mass effects.
• Using perturbative QCD techniques to compute two-loop corrections proportional to β₀, the first coefficient of the QCD beta function.
• Evaluating the resulting matrix elements in the context of direct CP asymmetry in B⁰ → π⁺π⁻ decays.
• Assessing theoretical uncertainties through renormalization scale variation and sensitivity to unknown nonperturbative parameters.

Experimental results

Research questions

• RQ1 How large are the O(α²ₛβ₀) perturbative corrections compared to the leading-order O(αₛ) contributions in B → ππ and B → πK decays?
• RQ2 To what extent do chirally enhanced power corrections affect the matrix elements and CP asymmetries in these decays?
• RQ3 How sensitive are the predictions for direct CP asymmetry in B⁰ → π⁺π⁻ to the choice of renormalization scale?
• RQ4 What is the impact of poorly known nonperturbative parameters on the reliability of CP asymmetry predictions at this order?

Key findings

• The O(α²ₛβ₀) corrections are often comparable in magnitude to the leading-order O(αₛ) corrections, indicating significant higher-order QCD effects.
• Direct CP asymmetries in B⁰ → π⁺π⁻ receive substantial contributions from these higher-order corrections, which are not negligible.
• Large uncertainties arise from renormalization scale dependence, particularly in the perturbative corrections.
• Poor knowledge of nonperturbative parameters further limits the precision of CP asymmetry predictions at this order.
• The inclusion of chirally enhanced power corrections is essential for a consistent description of the matrix elements at this perturbative order.