On the color suppressed contribution to $\bar{B_{d}^0} \rightarrow \, π^0 π^{0}

Abstract

The decay modes of the type $B\to \pi \pi$ are dynamically different. For the case $\overline{B_d^0}\to {\pi }^{+}{\pi }^{-}$ there is a substantial factorized contribution which dominates. In contrast, the decay mode $\overline{B_d^0}\to {\pi }^0{\pi }^0$ has a small factorized contribution, being proportional to a small Wilson coefficient combination. However, for the decay mode $\overline{B_d^0}\to {\pi }^0{\pi }^0$ there is a sizeable nonfactorizable (color suppressed) contribution due to soft (long distance) interactions, which dominate the amplitude. We estimate the branching ratio for the mode $\overline{B_d^0}\to {\pi }^0{\pi }^0$ in the heavy quark limit for the $b$- quark. In order to estimate color suppressed contributions we treat the energetic light ($u,d,s$) quark within a variant of Large Energy Effective Theory combined with a recent extension of chiral quark models in terms of model- dependent gluon condensates. We find that our calculated color suppressed amplitude is suppressed by a factor of order ${\Lambda }_{QCD}/m_b$ with respect to the factorizable amplitude, as it should according to QCD-factorization. Further, for reasonable values of the constituent quark mass and the gluon condensate, the calculated nonfactorizable amplitude for $\overline{B_d^0}\to {\pi }^0{\pi }^0$ 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 $\overline{B_d^0}\to {\pi }^0{\pi }^0$. A possible link to the triangle anomaly is discussed.

arXiv commentThe submitted Latex version correspond to 23 pages in ps-version and contains 4 figures

References in corpus (42)

• Weak Decays Beyond Leading Logarithms
• An effective field theory for collinear and soft gluons: heavy to light decays
• Heavy Quark Symmetry
• QCD Factorization for $B\to \pi \pi$ Decays: Strong Phases and CP Violation in the Heavy Quark Limit
• Summing Sudakov logarithms in B -> X_s + gamma in effective field theory
• Phenomenology of Heavy Meson Chiral Lagrangians
• Fat penguins and imaginary penguins in perturbative QCD
• The $\Delta S=1$ Effective Hamiltonian Including Next-to-Leading Order QCD and QED Corrections
• B -> M1 M2: Factorization, Charming Penguins, Strong Phases, and Polarization
• Heavy-to-Light Form Factors in the Final Hadron Large Energy Limit of QCD
• B->pi and B->K Transitions from QCD Sum Rules on the Light-Cone
• Chiral Dynamics and Heavy Quark Symmetry in a Toy Field Theoretic Model
• NNLO vertex corrections to non-leptonic B decays: Tree amplitudes
• ${\epsilon }^{\prime }/\epsilon$ at $O(p^4)$ in the Chiral Expansion
• A Constituent Quark-Meson Model for Heavy-Meson Processes
• Effective Meson Lagrangian with Chiral and Heavy Quark Symmetries from Quark Flavor Dynamics
• The Delta I = 1/2 Rule and B_K at O(p^4) in the Chiral Expansion
• Studying ${\epsilon }^{\prime }/\epsilon$ in the Chiral Quark Model: ${\gamma }_5$-Scheme Independence and NLO Hadronic Matrix Elements
• SCET sum rules for B->P and B->V transition form factors
• The $\Delta S=1$ Weak Chiral Lagrangian as the Effective Theory of the Chiral Quark Model
• Evolution of the Light Cone Distribution Function for a Heavy Quark
• Low--Energy Behavior of Two--Point Functions of Quark Currents
• Rare Decays $B^0\to D_s^{(\ast )+}{D}_s^{(\ast )-}$ and $B_s^0\to D^{(\ast )+}{D}^{(\ast )-}$ in Perturbative QCD Approach
• Annihilation effects in $B\to \pi \pi$ from QCD Light-Cone Sum Rules
• SU(3) Corrections to B -> D l nu Form Factors at O(1/M)
• Nonfactorizable contributions to the decay mode D^0 -> K^0 \bar{K^0}
• A Heavy-Light Chiral Quark Model
• New contribution to anomalous radiative $K^0$-decays
• A gluonic mechanism for B --> D eta'
• Color suppressed contributions to the decay modes B_{d,s} -> D_{s,d} D_{s,d}, B_{d,s} -> D_{s,d} D^*_{s,d}, and B_{d,s} -> D^*_{s,d} D^*_{s,d}
• B^+ --> D^{*+}_s gamma and B^+ --> D^{*+} gamma as Probes of V_{ub}
• The self-penguin contribution to $K\to 2\pi$
• Chiral symmetry and exclusive B decays in the SCET
• On the Colour Suppressed Decay Modes B^0 --> D_s^+ D_s^- and B_s^0 --> D^+ D^-
• The β-term for D^* --> D γwithin a heavy-light chiral quark model
• On the Short Distance Part of the QCD Anomaly Contribution to the b --> s eta' Amplitude
• Charmless Final State Interaction in B-> pi pi decays
• Factorization in Exclusive and Seminclusive Decays and Effective Theories for Massless Particles
• The Isgur-Wise Function within a Modified Heavy-Light Chiral Quark Model
• Non-factorizable contribtion to $\overline{B_d^0}\to {\pi }^0{D}^0$
• On the Decay Modes $\overline{B_{d,s}^0}\to \gamma D^{\ast 0}$
• $B\to \pi \pi$ decays: branching ratios and CP asymmetries

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