We study the decay $B^{+}\to K^{+}{K}^{-}{\pi }^{+}$ and investigate the angular distribution of $K^{+}{K}^{-}$ pairs with invariant mass below $1.1\mathrm{GeV}/c^2$. This region exhibits both a strong enhancement in signal and very large direct $CP$ violation. We construct a coherent sum model for the angular distribution of the $S$- and $P$-wave, and report the ratio of their amplitudes, the relative phase and the forward-backward asymmetry. We also report absolute differential branching fractions and direct $CP$ asymmetry for the decay in bins of $M_{K^{+}{K}^{-}}$ and the differential branching fractions in bins of $M_{K^{+}{\pi }^{-}}$. The results are based on a data sample that contains $772\times {10}^6$ $B\overline{B}$ pairs collected at the $\mathrm{\Upsilon }(4S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider. The result favors the presence of $S$- and $D$-waves in low $M_{K^{+}{K}^{-}}$ region to the detriment of a $P$-wave.

• Received 24 June 2022
• Accepted 3 February 2023

DOI:https://doi.org/10.1103/PhysRevD.107.032013

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Published by the American Physical Society