CP violation and kaon-pion interactions in B {r_arrow} K {pi}{sup +}{pi}{sup -} decays.

We study CP violation and the contribution of the strong kaon-pion interactions in the three-body B {yields} Kpi{sup +}pi{sup -} 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 Kpi 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*{sub 0}(1430) decay constant is found to be (32 {+-} 5) MeV. The additional phenomenological amplitudes are fitted to reproduce the Kpi effective mass and helicity angle distributions, the B {yields} K*(892)pi branching ratios and the CP asymmetries of the recent data from Belle and BABAR collaborations. We use also the new measurementmore » by the BABAR group of the phase difference between the B{sup 0} and [overline B]{sup 0} decay amplitudes to K*(892)pi. Our predicted B{sup {+-}} {yields} K*{sub 0}(1430)pi{sup {+-}}, K*{sub 0}(1430) {yields} K{sup {+-}}pi{sup {-+}} branching fraction, equal to (11.6 {+-} 0.6) x 10{sup -6}, is smaller than the result of the analyzes of both collaborations. For the neutral B{sup 0} decays, the predicted value is (11.1 {+-} 0.5) x 10{sup -6}. In order to reduce the large systematic uncertainties in the experimental determination of the B {yields} K*{sub 0}(1430)pi branching fractions, a new parametrization is proposed. It is based on the Kpi scalar form factor, well constrained by theory and experiments other than those of B decays.« less