Amplitude analysis of the $B^{+}\to {\pi }^{+}{\pi }^{+}{\pi }^{-}$ decay

Abstract

The results of an amplitude analysis of the charmless three-body decay $B^{+}\to {\pi }^{+}{\pi }^{+}{\pi }^{-}$, 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 $3{\text{fb}}^{-1}$ of $pp$ collisions recorded with the LHCb detector. The most challenging aspect of the analysis is the description of the behaviour of the ${\pi }^{+}{\pi }^{-}$ 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 $\rho (770{)}^0$, $\omega (782)$ and $\rho (1450{)}^0$ resonances in the ${\pi }^{+}{\pi }^{-}$ P-wave, the $f_2(1270)$ resonance in the ${\pi }^{+}{\pi }^{-}$ D-wave, and the ${\rho }_3(1690{)}^0$ resonance in the ${\pi }^{+}{\pi }^{-}$ F-wave. Significant $CP$-violation effects are observed in both S- and D-waves, as well as in the interference between the S- and P-waves. The results from all three approaches agree and provide new insight into the dynamics and the origin of $CP$-violation effects in $B^{+}\to {\pi }^{+}{\pi }^{+}{\pi }^{-}$ decays.

arXiv commentAll figures and tables, along with any supplementary material and additional information, are available at https://cern.ch/lhcbproject/Publications/p/LHCb-PAPER-2019-017.html (LHCb public pages)

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