The three body decaysB+→π+π−π+in perturbative QCD approach

Abstract

Abstract In this work, we study three body decays B + → π + π − π + in the perturbative QCD (pQCD) approach. The analysis is simplified into the one for two-body decays by introducing two-meson distribution amplitudes. We calculate both nonresonant and resonant contributions, and show the contribution to the B + → π + π − π + decays spectrum with respect to the dipion invariant mass M ( π + π − ) . Besides the usual factorizable diagrams, the non-factorizable and annihilation diagrams are also calculated analytically. The pQCD predictions for the branching ratios of B + → π + π − π + (nonresonant) are Br = 5.7 × 10 − 6 , the results of the resonant contributions are Br ( B + → π + ρ ( 770 ) ) = 8.9 × 10 − 6 . The above pQCD predictions agree well with current available data. We also predict another resonant contribution Br ( B + → π + f 0 ( 980 ) ) = 7.3 × 10 − 6 , but with large error. We still do not have a clear understanding about the inner structure of the scalar mesons f 0 . Further improvement in theory and experiments are expected.