Amplitude analysis of the B+ -> pi+ pi+ pi- decay

The results of an amplitude analysis of the charmless three-body decay B+→ π+π+π−, in which CP -violation effects are taken into account, are reported. The analysis is based on a data sample corresponding to an integrated luminosity of 3 fb−1 of pp collisions recorded with the LHCb detector. The most challenging aspect of the analysis is the description of the behaviour of the π+π− S-wave contribution, which is achieved by using three complementary approaches based on the isobar model, the K-matrix formalism, and a quasi-model-independent procedure. Additional resonant contributions for all three methods are described using a common isobar model, and include the ρ(770)0, ω(782) and ρ(1450)0 resonances in the π+π− P-wave, the f2(1270) resonance in the π +π− D-wave, and the ρ3(1690) 0 resonance in the π+π− F-wave. Significant CP -violation effects are observed in both Sand D-waves, as well as in the interference between the Sand P-waves. The results from all three approaches agree and provide new insight into the dynamics and the origin of CP -violation effects in B+→ π+π+π− decays. Published in Phys. Rev. D 101 (2020) 012006 c © 2020 CERN for the benefit of the LHCb collaboration. CC-BY-4.0 licence. †Authors are listed at the end of this paper. ar X iv :1 90 9. 05 21 2v 2 [ he pex ] 2 3 Ja n 20 20