We construct a low-energy effective field theory that permits the complete treatment of isospin-breaking effects in nonleptonic weak interactions to next-to-leading order. To this end, we enlarge the chiral Lagrangian describing strong and ∆S = 1 weak interactions by including electromagnetic terms with the photon as additional dynamical degree of freedom. The complete and minimal list of local...

Chiral perturbation theory, the low energy effective theory of the strong interactions for the light pseudoscalar degrees of freedom, is based on effective Lagrangian techniques and is an expansion in the powers of the external momenta and the powers of the quark masses, which correct the soft-pion theorems. Our primary emphasis will be on the problem of ππ scattering. After briefly reviewing t...

We prove that CP violating rate difference ∆(B̄0 → π+π−) = Γ(B̄0 → π+π−)− Γ(B0 → π−π+) is related to ∆(B̄0 → π+K−) = Γ(B̄0 → π+K−)− Γ(B0 → π−K+) in the three generation Standard Model. Neglecting small annihilation diagrams, and in the SU(3) symmetry limit, we show ∆(B̄0 → π+π−) = −∆(B̄0 → π+K−). The SU(3) breaking effects are estimated using factorization approximation, and yield ∆(B̄0 → π+π−) ≈ −(fπ...

We derive model independent lower bounds on the CKM parameters (1− ρ̄) and η̄ as functions of the mixing-induced CP asymmetry S in B → ππ and sin 2β fromB → ψKS. The bounds do not depend on specific results of theoretical calculations for the penguin contribution to B → ππ. They require only the very conservative condition that a hadronic phase, which vanishes in the heavy-quark limit, does not e...

The expression for the (π + π −) atom lifetime is derived within the Bethe-Salpeter approach. First-order perturbative corrections due to the contribution of strong interactions are taken into account. It is demonstrated that the atom lifetime can be expressed in terms of the solutions of the Coulombic problem (the wave function of the 1S state at the origin Ψ 1 (0), the binding energy of the S...

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...

Strong isospin-breaking (IB) effects in CP-even and CP-odd K → ππ decays are computed to next-to-leading order (NLO) in the chiral expansion. The impact of these corrections on the magnitude of the ∆I = 1/2 Rule and on the size of the IB correction, ΩIB, to the gluonic penguin contribution to ǫ /ǫ are discussed. In the presence of IB, the standard isospin decomposition of the K → ππ, K → ππ, ππ...

Roy’s equations are used to check if the scalar-isoscalar ππ scattering amplitudes fitted to experimental data fulfill crossing symmetry conditions. It is shown that the amplitudes describing the “down-flat” phase shift solution satisfy crossing symmetry below 1 GeV while the amplitudes fitted to the “up-flat” data do not. In this way the long standing ”up-down” ambiguity in the phenomenologica...

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...