We report on a dispersion relation for the γγ → (ππ)I S-wave in isospin I emphasizing the low energy region. The f0(980) signal that emerges in γγ → ππ is also discussed. Our results could be used to distinguish between different ππ isoscalar S-wave parameterizations. We also calculate the width of the σ resonance to γγ and obtain the value Γ(σ → γγ) = (1.68±0.15) KeV. Finally, we elaborate on ...

Scalar-isoscalar mesons are studied using an unitary model in three channels: ππ, KK and an effective 2π2π. All the solutions, fitted to the ππ and KK data, exhibit a wide f0(500), a narrow f0(980) and two relatively narrow resonances, lying on different sheets between 1300 MeV and 1500 MeV. These latter states are similar to the f0(1370) and f0(1500) seen in experiments at CERN. Branching rati...

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...

We present the analytical results for the K → 3π final state interaction phases at next-to-leading order (NLO) in CHPT. We also study the recent proposal of Cabibbo to measure the ππ scattering lengths combination a0−a2 from the cusp effect in the π π energy spectrum at threshold for K → πππ and KL → π ππ, and we give the relevant formulas to describe it at NLO. We estimate the theoretical unce...

The ππ interactions are one of the main sources of information on low energy physics. Their knowledge in scalar-isoscalar channel allows us to investigate scalar meson spectroscopy and to test the predictions of many theoretical models. Amplitudes of the ππ interactions should fulfill some basic conditions like unitarity and crossing symmetry. Described in 1) three-coupled channel amplitudes fo...

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, ...

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...