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Non-leptonic decays in an extended chiral quark model
High Energy Physics - Phenomenology · Submitted 7 Dec 2012
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim 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} $.
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The abstract, sentence by sentence
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} $.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We consider the color suppressed (nonfactorizable) amplitude for the decay mode $\bar{B_{d}^0} \rightarrow \pi^0 \pi^{0} $. | contribution 0.91 | 0.52 | 0.04 | asserted 0.51 |
| s1 | 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. | method 1.00 | 0.83 | 0.03 | asserted 0.99 |
| s2 | 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. | result 0.97 | 0.90 | 0.22 | asserted 1.00 |
| s3 | 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. | result 0.91 | 0.91 | 0.39 | hedged possibility 0.93 |
| s4 | Unfortunately, the color suppressed amplitude is very sensitive to the values of these model dependent parameters. | limitation 1.00 | 0.73 | 0.10 | asserted 1.00 |
| s5 | 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} $. | limitation 0.90 | 0.73 | 0.41 | asserted 0.99 |
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Original 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} $.
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