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We study the contribution of the strong interaction between the two pions inS- and P-waves to the weak B --> pion pion kaon decay amplitudes. Theinterference between these two waves is analyzed in the pion-pion effectivemass range of the rho(770) and f0(980) resonances. We use a unitary pion-pionand antikaon-kaon coupled-channel model to describe the S-wave interactions anda Breit-Wigner function for the P-wave amplitude. The weak B-decay amplitudes,obtained from QCD factorization, are supplemented with charming penguincontributions in both waves. The four complex parameters of these long distanceterms are determined by fitting the model to the BaBar and Belle data onB^{+,-,0} --> pi+ pi- K^{+,-,0} branching fractions, CP asymmetries, pion-pioneffective mass and helicity-angle distributions. This set of data, and inparticular the large direct CP-asymmetry for B^{+,-} --> rho0(770) K^{+,-}decays, is well reproduced.  The interplay of charming penguin amplitudes and the interference of S- andP-waves describes rather successfully the experimental S and A values of theCP-violating asymmetry for both B0 --> f0(980) K0S and B0 --> rho0(770) K0Sdecays.Comment: 12 pages, 7 figures, subsection VD, Appendix A and one reference  adde

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

Interference between<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>f</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mn>980</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>ρ</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>770</mml:mn><mml:msup><mml:mo stretchy="false">)</mml:mo><mml:mn>0</mml:mn></mml:msup></mml:math>resonances …

Interference betweenf0(980)andρ(770)0resonances …