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

摘要

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