Angular analysis of the low $K^{+}{K}^{-}$ invariant mass enhancement in $B^{+}\to K^{+}{K}^{-}\ddot{I}{€}^{+}$ decays

Abstract

We study the decay $B^{+}\to K^{+}{K}^{-}\ddot{I}{€}^{+}$ and investigate the angular distribution of $K^{+}{K}^{-}$ pairs with invariant mass below $1.1$ 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 $S$- 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 $M_{K^{+}\ddot{I}{€}^{-}}$. The results are based on a data sample that contains $772\times 10^6$ $B\bar{B}$ pairs collected at the $\hat{I}\yen (4S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider. The measured overall branching fraction and the direct $CP$ asymmetry are $(5.38\pm 0.40\pm 0.35)\times 10^{-6}$ and $-0.170\pm 0.073\pm 0.017$, respectively, where the first uncertainties are statistical and the second are systematic.

13 pages, 8 figures