Resonances and final state interactions (FSI) play a role in the formation of CP violation (CPV) constrained by CPT invariance. We provide a general formulation of CPV including resonances and FSI starting from the CPT constraint. Our discussion is elaborated within a simple B decay model with the ρ and f0(980) resonances plus a non resonant background including the ππ → KK coupled amplitude. We consider few illustrative examples to show the interference patterns appearing in the CP asymmetry, namely, that from the ρ resonance plus a non-resonant amplitude, and that from the interference of the ρ and f0 (980) resonances. We perform the fit of the CP asymmetry for the charmless three-body B

No abstract

No abstract

The scalar three-body Bethe-Salpeter equation, with zero-range interaction, is solved in Minkowski space by direct integration of the four-dimensional integral equation. The singularities appearing in the propagators are treated properly by standard analytical and numerical methods, without relying on any ansatz or assumption. The results for the binding energies and transverse amplitudes are compared with the results computed in Euclidean space. A fair agreement between the calculations is found.

We investigate the response of the bound state structure of a two-boson system, within a Yukawa model with a scalar boson exchange, to the inclusion of the crossladder contribution to the ladder kernel of the Bethe-Salpeter equation. The equation is solved by means of the Nakanishi integral representation and light-front projection. The valence light-front wave function and the elastic electromagnetic form factor beyond the impulse approximation, with the inclusion of the two-body current, generated by the cross-ladder kernel, are computed. The valence wave function and electromagnetic form factor, considering both ladder and ladder plus crossladder kernels, are studied in detail. Their asymptotic forms are found to be quite independent of the inclusion of the cross-ladder kernel, for a given binding energy. The asymptotic decrease of form factor agrees with the counting rules. This analysis can be generalized to fermionic systems, with a wide application in the study of the meson structure.

No abstract

Charge Parity asymmetry in charmless B meson decays is a key issue to be understood. Many theoretical calculations have been performed using short distance factorization approaches which, in general, do not take into account the CPT invariance constraint. For each channel with CP violation there is an equal amount of CP asymmetry in another channel or other channels, with an opposite sign. This happens if these channels are coupled through final state interactions (FSI). In the specific process B → P V , involving one pseudo-scalar and one vector particle in the final state, we argue that the CP asymmetry, inherent from a short distance mechanism, could be suppressed due to the CPT constraint. In this case, we propose a sensitive and practical experimental method to identify even a small CP asymmetry, which provides the values for A CP without the need for an amplitude analysis. This method, if applied directly to data, will enable to extract the CP asymmetry information in a model independent way and check to which extend the suggested suppression due to the CPT constraint is verified. * pmagalhaes@cbpf.br

The ladder Bethe-Salpeter Equation of a bound (1/2) + system, composed by a fermion and a scalar boson, is solved in Minkowski space, for the first time. The formal tools are the same already successfully adopted for two-scalar and two-fermion systems, namely the Nakanishi integral representation of the Bethe-Salpeter amplitude and the light-front projection of the fulfilled equation. Numerical results are presented and discussed for two interaction kernels: i) a massive scalar exchange and ii) a massive vector exchange, illustrating both the correlation between binding energies and the interaction coupling constants, as well as the valence content of the interacting state, through the valence probabilities and the light-front momentum distributions. In the case of the scalar exchange, an interesting side effect, to be ascribed to the repulsion generated by the small components of the Dirac spinor, is pointed out, while for the vector exchange the manifestation of the helicity conservation opens new interesting questions to be addressed within a fully non-perturbative framework, as well as the onset of a scale-invariant regime.