J.O. Eeg

ε′ε at O(p4) in the chiral expansion

After updating the determination of the combination of Kobayashi-Maskawa elements Im VtdVts∗ according to our new estimate of the parameter BK, we study the CP-violating ratio e′e by means of hadronic matrix elements computed to O(p4) in the chiral expansion. It is the first time that this order in chiral perturbation theory is included. We also discuss the relevance of some O(p2) terms that are generally neglected in the calculation of the electroweak penguin matrix elements. The most important effect of this improved analysis is the substantial reduction (20%) of the leading electroweak penguin matrix element and accordingly a reduced cancelation between the electroweak and gluon penguin contributions. The ratio e′e is thus larger than previously estimated and its predicted value enjoys a smaller uncertainty. We find e′/e = 1.7−1.0+1.4 × 10−3. Values positive and of the order of 10−3 are therefore preferred.

The ΔS = 1 weak chiral lagrangian as the effective theory of the chiral quark model

We use the chiral quark model to construct the complete O(p2) weak ΔS = 1 chiral lagrangian via the bosonization of the ten relevant operators of the effective quark lagrangian. The chiral coefficients are given in terms of fπ the quark and gluon condesates and the scale-dependent NLO Wilson coefficients of the corresponding operators; in addition, they depend on the constituent quark mass M, a parameter characteristic of the model. All contributions of order Nc2 as well as Nc and αsNc are included. The γ5-scheme dependence of the chiral coefficients, computed via dimensional regularization, and the Fierz transformation properties of the operator basis are discussed in detail. We apply our results to the evaluation of the hadronic matrix elements for the decays K → 2π, consistently including the renormalization induced by the meson loops. The effect of this renormalization is sizable and introduces a long-distance scale dependence that matches in the physical amplitudes the short-distance scale dependence of the Wilson coefficients.

Two Loop Diagrams for the Electric Dipole Moment of the Neutron

CP-violating two-loop Feynman diagrams for the electric dipole moment of the neutron are considered in the framework of the Kobayashi-Maskawa model. It is shown that leading logarithmic contributions ∼ 1n|MW2| are cancelled by a twofold GIM mechanism. The remaining logarithms of heavy-quark masses are called “relics of short-distance effects”. It is also found that the calculated contributions are complementary and of the same order of magnitude as some corresponding long-distance contributions considered by other authors. The electric dipole moment of the neutron is estimated not to exceed |Dn/e| ∼10−32 cm. Some details of two-loop integrations are presented, in particular the effectiveness of dimensional regularization in calculating certain individual diagrams.

The ΔI = 12 rule and BK at O(p4) in the chiral expansion

We calculate the hadronic matrix elements to O(p4) in the chiral expansion for the (ΔS=1) Ko → 2π decays and the (ΔS = 2) k0−K0 oscillation. This is done within the framework of the chiral quark model. The chiral coefficients thus determined depend on the values of the quark and gluon condensates and the constituent quark mass. We show that it is possible to fit the ΔI = 12 rule of kaon decays with values of the condensates close to those obtained by QCD sum rules. The renormalization invariant amplitudes are obtained by matching the hadronic matrix elements and their chiral corrections to the short-distance NLO Wilson coefficients. For the same input values, we study the parameter BK of kaon oscillation and find BK = 1.1 ± 0.2. As an independent check, we determine BK from the experimental value of the KL-KS mass difference by using our calculation of the long-distance contributions. The destructive interplay between the short- and long-distance amplitudes yields BK = 1.2 ± 0.1, in agreement with the direct calculation.

Off-shells s→d transitions in K-decays

Abstract In an attempt to go beyond the free quark mass-shell, we reveal new contributions to K -meson decays. We account for them by using an effective low-energy QCD, advocated by many authors, where the quarks are coupled to the pseudoscalar mesons π , K , η . These couplings are due to their Goldstone character, and reflect chiral-symmetry breaking. Within this scheme we find explicitly that, for the decays K → ππ and K → γγ , the physical effects of operators involving (i γ ·D− m q ) are not zero, contrary to current statements. To be more specific, one obtains a zero effect only in the limit when the quark-meson interactions are switched off, that is for ƒ π →∞ . Numerically, we find weak impact on the CP -conserving K → ππ amplitude, while the impact on K → γ γ is substantial in the CP -violating case.

A Heavy light chiral quark model

We present a new chiral quark model for mesons involving a heavy and a light (anti-) quark. The model relates various combinations of a quark - meson coupling constant and loop integrals to physical quantities. Then, some quantities may be predicted and some used as input. The extension from other similar models is that the present model includes the lowest order gluon condensate of the order (300 MeV)^4 determined by the mass splitting of the 0^- and the 1^- heavy meson states. Within the model, we find a reasonable description of parameters such as the decay constants f_B and f_D, the Isgur-Wise function and the axial vector coupling g_A in chiral perturbation theory for light and heavy mesons.

New contribution to anomalous radiative K0-decays

Abstract We present a new contribution to the K L → γγ amplitude, which is O (p 4 ) within the counting rules of chiral perturbation theory. This direct (non-pole) amplitude, obtained from short-distance s → dγ quark diagrams of order eG F α s π , and similar s → dγγ diagrams, can account for about half of the experimental amplitude. Closely following the description of the π 0 → γγ and K L → γγ processes in the variants of the same low-energy QCD, we find that both of these processes are anomalous in the same sense. Then, by the anomaly-matching principle, we arrive from the chiral-quark to the bosonic counterparts for both of these processes. In this way we add the K L → γγ decay to the existing list of anomalous radiative prosesses.

Non-factorizable contributions to

It is pointed out that decays of the type

Direct CP violation in KL,S→2γ for a large top mass

B \to D \bar{D}

Short-distance CP-violating contributions to the KL→π0e+e− decay

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