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

The first amplitude analysis of the $B^\pm \to \pi^\pm K^+ K^-$ decay is reported based on a data sample corresponding to an integrated luminosity of 3.0 fb$^{−1}$ of $pp$ collisions recorded in 2011 and 2012 with the LHCb detector. The data is found to be best described by a coherent sum of five resonant structures plus a nonresonant component and a contribution from $\pi \pi \leftrightarrow KK$ $S$-wave rescattering. The dominant contributions in the $\pi^\pm K^\mp$ and $K^+ K^−$ systems are the nonresonant and the $B^ \pm \to \rho (1450)^0 \pi^\pm$ amplitudes, respectively, with fit fractions around 30$%$. For the rescattering contribution, a sizeable fit fraction is observed. This component has the largest $CP$ asymmetry reported to date for a single amplitude of $(−66 \pm 4 \pm 2) \%$, where the first uncertainty is statistical and the second systematic. No significant $CP$ violation is observed in the other contributions.