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CP violation and kaon-pion interactions in B --> K pi+ pi- decays

We study CP violation and the contribution of the strong kaon-pion interactions in the three body B --> K pi+ pi- decays. We extend our recent work on the effect of the two-pion S- and P-wave interactions to that of the corresponding kaon-pion ones. The weak amplitudes have a first term derived in QCD factorization and a second one as a phenomenological contribution added to the QCD penguin amplitudes. The effective QCD coefficients include the leading order contributions plus next-to-leading order vertex and penguins corrections. The matrix elements of the transition to the vacuum of the kaon-pion pairs, appearing naturally in the factorization formulation, are described by the strange K pi scalar (S-wave) and vector (P-wave) form factors. These are determined from Muskhelishvili-Omnes coupled channel equations using experimental kaon-pion T-matrix elements, together with chiral symmetry and asymptotic QCD constraints. From the scalar form factor study, the modulus of the K*_0(1430) decay constant is found to be (32 +/- 5) MeV. The additional phenomenological amplitudes are fitted to reproduce the K pi effective mass and helicity angle distributions, the B --> K*(892) pi branching ratios and the CP asymmetries of the recent data from Belle and BaBar collaborations. We use also the new measurement by the BaBar group of the phase difference between the B0 and B0bar decay amplitudes to K*(892) pi. Our predicted B+/- --> K*_0(1430) pi+/-, K*_0(1430) --> K+/- pi-\+ branching fraction, (11.6 +/- 0.6) 10^{-6}, is smaller than the result of the analyzes of both collaborations. For the neutral B0 decays, the predicted value is (11.1 +- 0.5) 10^{-6}. In order to reduce the large systematic uncertainties in the experimental determination of the B --> K*_0(1430) pi branching fractions, a new parametrization is proposed.