Amplitude analysis of $B^{+}\to K^{+}{\pi }^{+}{\pi }^{-}$ decays

Abstract

The branching fractions and quasi-two-body $CP$-violating asymmetries of intermediate states obtained through an amplitude analysis of the charmless three-body decay $B^{+}\to K^{+}{\pi }^{+}{\pi }^{-}$ are reported. The analysis is based on $pp$ collision data at centre-of-mass energies $\sqrt{s}=7$ and $8\text{TeV}$ recorded with the LHCb detector, corresponding to an integrated luminosity of $3{\text{fb}}^{-1}$. The most challenging aspect of the amplitude modelling lies in the description of the dominant $K^{+}{\pi }^{-}$ and ${\pi }^{+}{\pi }^{-}$ S-wave contributions. This is achieved by three complementary approaches based on a physically motivated analytic model built on the isobar approximation, the K-matrix formalism, and a quasi-model-independent procedure in which overlapping crossing partial waves are simultaneously studied. In addition, alternative sets of results are presented, considering the ${\pi }^{+}{\pi }^{-}$ final state to manifest either through direct $\omega (782)$ decays or $\rho (770{)}^0\text{-}\omega (782)$ mixing. The most precise measurements of branching fractions and $CP$ asymmetries are obtained for the vast majority of intermediate states, establishing firmer reference points against which to cleanly probe model-independent physics beyond the Standard Model. The results from all three approaches agree and provide new insight into strong dynamics and the origin of $CP$-violation effects in $B^{+}\to K^{+}{\pi }^{+}{\pi }^{-}$ decays.

All figures and tables, along with machine-readable versions and any supplementary material and additional information, are available at https://lhcb-glance.cern.ch/alcm/public/analysis/full-details/1622/ (LHCb public pages)