Observation of several sources of $C\text{\hspace{0.17em}⁣}P$ violation in $B^{+}\text{\hspace{0.17em}⁣}\to K^{+}{\pi }^{+}{\pi }^{-}$ decays

An amplitude analysis of $B^{+}\text{\hspace{0.17em}⁣}\to K^{+}{\pi }^{+}{\pi }^{-}$ decays is presented in which six $C\text{\hspace{0.17em}⁣}P$-violating phenomena are judged to be of significance for the first time. This analysis is based on $pp$ collision data recorded with the LHCb detector in 2011-2012, corresponding to an integrated luminosity of $3{\text{fb}}^{-1}$. Quasi-two-body $C\text{\hspace{0.17em}⁣}P$ violation in $B^{+}\text{\hspace{0.17em}⁣}\to \rho (770{)}^0{K}^{+}$ decays is discovered, while $C\text{\hspace{0.17em}⁣}P$ violation at amplitude level is established in $B^{+}\text{\hspace{0.17em}⁣}\to f_2(1270)K^{+}$ decays. First evidence for $C\text{\hspace{0.17em}⁣}P$ violation is reported in both the fully elastic S-wave $\pi \pi$-$\pi \pi$ rescattering region and also for any decay involving a spin-3 resonance. Additionally, significant $C\text{\hspace{0.17em}⁣}P$-violation effects are identified in the interference between different $\pi \pi$ partial waves, with observation in S-P wave interference and evidence in S-D wave interference, both of which must be driven by long-distance interactions.