Complete next-to-leading (chiral) order (NLO) expressions for the strong isospin-breaking (IB) contributions in K → ππ are used to discuss (1) for CP-even, the impact on the magnitude of the ∆I = 1/2 Rule, and (2) for CP-odd, the strong IB correction, Ωst, for the gluonic penguin contribution to ǫ /ǫ, with particular emphasis on the strong low-energy constant (LEC) and loop contributions, numer...

In the presence of penguin contributions, the indirect CP asymmetry in B(t) → ππ measures sin(2α + 2θ), where 2θ parametrizes the size of the penguin “pollution.” We present a new upper bound on |2θ|, involving also the measurement of B → ππ, along with an upper bound on or a measurement of BR(B → ππ)+BR(B0 → ππ). The new bound is stronger than those previously discussed in the literature. Inde...

A ππ, K̄K, and ρρ(ωω) fully coupled channel model is used to predict the lowest isospin S, P, D, F-wave phase shifts and inelasticities for elastic ππ scattering from threshold to 2.0 GeV. As input the S-matrix is required to exhibit poles corresponding to the meson resonance table of the Particle Data Group. As expected, the ππ inelasticity is very strongly related to the opening of the K̄K chan...

We have calculated the KK̄ → KK̄ scattering amplitude to next to leading order in Chiral Perturbation Theory. Then, making use of a unitarization procedure with one or several coupled channels (ππ,KK̄ in our case) we have calculated the ππ → ππ, ππ → KK̄ and KK̄ → KK̄ S and P waves in good agreement with the experiment up to √ s ≃ 1.2 GeV. The ππ scattering lengths with isospin and spin (I,J) equal t...

The observation of a cusp-like structure in the M00 invariant mass distribution in the decay K ± → π±π0π0 by the NA48/2 experiment at CERN has given a renewed interest in the ππ scattering lengths. We report the result of a study of a partial sample of 2.3 × 10 decays, the observation of an anomaly in the ππ mass spectrum in the region around M00 = m+, where m+ is the mass of the charged pion, ...

A general prescription for the construction of ππ interaction potentials which preserve scattering length constraints from chiral symmetry when iterated in scattering equations is derived. The prescription involves only minor modifications of typical meson-exchange models, so that coupling constants and cutoff masses in the models are not greatly affected. Calculations of s-wave ππ scattering a...

In the last few years it has become possible to study low energy ππ scattering in kaon decays to three pions, thanks to the high statistics measurement of K → πππ decays performed by the NA48/2 experiment at the CERN SPS. At the ππ threshold, the ππ mass spectrum exhibits a Wigner-cusp, from which the S-wave ππ scattering lengths are extracted with high precision. This measurement is complement...

A principal decay mode considered for the measurement of the angle α, is B d(t) → ππ. Unfortunately, this mode suffers from a well-known problem: penguin contributions may be large [2], and their presence will spoil the clean extraction of α. In the presence of penguin amplitudes, the CP asymmetry in B d(t) → ππ does not measure sin 2α, but rather some effective (“polluted”) angle 2αeff . We ma...

Measurements of the time-dependent CP asymmetry in the decay B d(t) → ππ and its charge conjugate by the BELLE and BABAR collaborations currently yield C ππ = −0.46 ± 0.13 and S ππ = −0.74 ± 0.16, characterizing the direct and mixing-induced CP asymmetries, respectively. We study the implication of these measurements on the CKM phenomenology taking into account the available information in the ...

The large ratio of color-suppressed tree amplitude to color-allowed one in B → ππ decays is difficult to understand within the Standard Model, which is known as the “B → ππ puzzle”. The two tree diagrams contain the upand charm-quark component of penguin amplitude, Puc, which cannot be separated by measuring B → ππ decays alone. We show that the measurements of the branching ratio and direct CP...