Non-leptonic decays in an extended chiral quark model

TL;DR

This paper models nonfactorizable amplitudes in B meson decays using an extended chiral quark model combined with effective theories, showing suppression consistent with QCD and potential agreement with experimental data.

Contribution

It introduces a novel approach combining Large Energy Effective Theory with extended chiral quark models to calculate nonfactorizable decay amplitudes.

Findings

Calculated amplitude suppressed by Λ_QCD/m_b as expected from QCD.

Model can match experimental values with reasonable parameter choices.

Amplitude sensitivity requires fine-tuning of model parameters.

Abstract

We consider the color suppressed (nonfactorizable) amplitude for the decay mode $\bar{B_{d}^0} \rightarrow \pi^0 \pi^{0} $. We treat the $b$-quark in the heavy quark limit and the energetic light ($u,d,s$) quarks within a variant of Large Energy Effective Theory combined with an extension of chiral quark models. Our calculated amplitude for $\bar{B_{d}^0} \rightarrow \pi^0 \pi^{0} $ is suppressed by a factor of order $\Lambda_{QCD}/m_b$ with respect to the factorized amplitude, as it should according to QCD-factorization. Further, for reasonable values of the (model dependent) gluon condensate and the constituent quark mass, the calculated nonfactorizable amplitude for $\bar{B_{d}^0} \rightarrow \pi^0 \pi^{0} $ can easily accomodate the experimental value. Unfortunately, the color suppressed amplitude is very sensitive to the values of these model dependent parameters. Therefore fine-tuning is necessary in order to obtain an amplitude compatible with the experimental result for $\bar{B_{d}^0} \rightarrow \pi^0 \pi^{0} $.