Amplitude analysis of the $B^{+}\to \ddot{I}{€}^{+}\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ decay

Abstract

The results of an amplitude analysis of the charmless three-body decay $B^{+}\to \ddot{I}{€}^{+}\ddot{I}{€}^{+}\ddot{I}{€}^{-}$, 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 $\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ 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 $\ddot{I}(770{)}^0$, $\ddot{I}‰(782)$ and $\ddot{I}(1450{)}^0$ resonances in the $\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ P-wave, the $f_2(1270)$ resonance in the $\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ D-wave, and the $\ddot{I}{}_3(1690{)}^0$ resonance in the $\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ 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 $B^{+}\to \ddot{I}{€}^{+}\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ decays.

All 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)