The self-penguin contribution to K→2πK \to 2 \pi

We consider the contribution to $K \rightarrow 2 \pi$ decays from the non-diagonal s \ra d quark transition amplitude. First, we calculate the most important part of the $s \rightarrow d$ transition, the so-called self-penguin amplitude $\sim G_F \alpha_s$, including the heavy top-quark case. Second, we calculate the matrix element of the $s \rightarrow d$ transition for the physical $K \rightarrow 2 \pi$ process. This part of the analysis is performed within the Chiral Quark Model where quarks are coupled to the pseudoscalar mesons. The CP-conserving self-penguin contribution to $K \rightarrow 2\pi$ is found to be negligible. The obtained contribution to $\epsilon'/\epsilon$ is sensitive to the values of the quark condensate $$ and the constituent quark mass $M$. For reasonable values of these quantities we find that the self-penguin contribution to $\epsilon'/\epsilon$ is 10-15% of the gluonic penguin contribution and has the same sign. Given the large cancellation between gluonic and electroweak penguin contributions, this means that our contribution is of the same order of magnitude as $\epsilon'/\epsilon$ itself.Comment: Latex, 12 pages, 2 figure

The \beta-term for D^* --> D \gamma within a heavy-light chiral quark model

We present a calculation of the \beta-term for D^* --> D gamma within a heavy-light chiral quark model. Within the model, soft gluon effects in terms of the gluon condensate with lowest dimension are included. Also, calculations of 1/m_c corrections are performed. We find that the value of \beta is rather sensitive to the constituent quark mass compared to other quantities calculated within the same model. Also, to obtain a value close to the experimental value, one has to choose a constituent light quark mass larger than for other quantities studied in previous papers. For a light quark mass in the range 250 to 300 MeV and a quark condensate in the range -(250-270 MeV)^3 we find the value (2.5 +- 0.6) GeV^-1. This value is in agreement with the value of \beta extracted from experiment 2.7 +- 0.2 GeV^-1.Comment: 16 pages, 5 figure

The Isgur-Wise Function within a Modified Heavy-Light Chiral Quark Model

We consider the Isgur-Wise function xi(omega) within a new modified version of a heavy-light chiral quark model. While early versions of such models gave too small absolute value of the slope, namely xi'(1) of about -0.4 to -0.3, we show how extended version(s) may lead to values around -1, in better agreement with recent measurements. This is obtained by introducing a new mass parameter in the heavy quark propagator. We also shortly comment on the consequences for the decay modes B --> D D-bar.Comment: 20 pages, 7 PS figure, LaTe

Non-leptonic decays in an extended chiral quark model

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 $\bar{B_{d}^0} \rightarrow \pi^0 \pi^{0}$.Comment: 10 pages, 6 figures. Presented at QCD@work, Lecce, Italy, june 201

Non-factorizable contributions to Bd0ˉ→Ds(∗)Ds(∗)ˉ\bar{B^0_d} \to D_s^{(*)} \bar{D_s^{(*)}}

It is pointed out that decays of the type $B \to D \bar{D}$ have no factorizable contributions, unless at least one of the charmed mesons in the final state is a vector meson. The dominant contributions to the decay amplitudes arise from chiral loop contributions and tree level amplitudes generated by soft gluon emissions forming a gluon condensate. We predict that the branching ratios for the processes $\bar B^0 \to D_s^+ D_s^-$, $\bar B^0 \to D_s^{+*} D_s^-$ and $\bar B^0 \to D_s^+ D_s^{-*}$ are all of order $(3- 4) \times 10^{-4}$, while $\bar B^0 \to D_s^{+*} D_s^{-*}$ has a branching ratio 5 to 10 times bigger. We emphasize that the branching ratios are sensitive to $1/m_c$ corrections.Comment: 4 pages, 4 figures. Based on talk by J.O. Eeg at BEACH 2004, 6th international conference on Hyperons, Charm and Beauty Hadrons, Illionois Institute of Technology, Chicago, june. 27 - july 3, 200

Non-factorizable contribtion to Bd0ˉ→π0D0\bar{B_{d}^0} \to \pi^0 D^{0}

The decay modes of the type $B \to \pi \, D$ are dynamically different. For the case $\bar{B_{d}^0} \to \pi^- D^{+}$ there is a substantial factorized contribution which dominates. In contrast, the decay mode $\bar{B_{d}^0} \to \pi^0 D^{0}$ has a small factorized contribution, being proportional to a very small Wilson coefficient combination. In this paper we calculate the relevant Wilson coefficients at one loop level in the heavy quark limits, both for the $b$-quark and the $c$-quark. We also emphasize that for the decay mode $\bar{B_{d}^0} \to \pi^0 D^{0}$ there is a sizeable non-factorizable contribution due long distance interactions, which dominate the amplitude. We estimate the branching ratio for this decay mode within our framework, which uses the heavy quark limits, both for the $b$- and the $c$-quarks. In addition, we treat energetic light ($u,d,s$) quarks within a variant of Large Energy Effective Theory and combine this with a new extension of chiral quark models. For reasonable values of the model dependent parameters of our model can account for at least 3/4 of the amplitude needed to explain the experimental branching ratio $\simeq 2.6 \times 10^{-4}$.Comment: 23 pages, 4 figures, 39 reference