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CP violation and strong pion-pion interactions in the weak B charged decays into three charged pions

An analysis of charged B decay data in a quasi two-body decay into a charged pion plus a S, P,or D state of two charged pions is performed in the QCD factorization framework. The short distance amplitudes are calculated including next-to-leading order corrections in the strong coupling constant for vertex and penguin contributions. The long distance amplitudes due to the two charged pion final state interactions are described by the pion non-strange scalar and vector form factors for the two-pion S- and P-wave states, respectively and by a relativistic Breit-Wigner formula for the D-wave state. We achieve a good fit of the data with only three parameters for the S wave, one for the P wave and one for the D wave. Our model gives a unified unitary description of the three scalar resonances, f_0(600), f_0(980) and f_0(1400) in terms of the pion scalar form factor. We predict for the B to f_2(1270) transition form factor a value of 0.098+-0.007 at a momentum transfer square equal to the pion-mass square.