Amplitude analysis of $B^{+}\to J/\ddot{I}ˆ\ddot{I}•K^{+}$ decays

Abstract

The first full amplitude analysis of $B^{+}\to J/\ddot{I}ˆ\ddot{I}•K^{+}$ with $J/\ddot{I}ˆ\to \hat{I}{¼}^{+}\hat{I}{¼}^{-}$, $\ddot{I}•\to K^{+}{K}^{-}$ decays is performed with a data sample of 3 fb${}^{-1}$ of $pp$ collision data collected at $\sqrt{s}=7$ and $8$ TeV with the LHCb detector. The data cannot be described by a model that contains only excited kaon states decaying into $\ddot{I}•K^{+}$, and four $J/\ddot{I}ˆ\ddot{I}•$ structures are observed, each with significance over $5$ standard deviations. The quantum numbers of these structures are determined with significance of at least $4$ standard deviations. The lightest has mass consistent with, but width much larger than, previous measurements of the claimed $X(4140)$ state. The model includes significant contributions from a number of expected kaon excitations, including the first observation of the $K^{\ast }(1680{)}^{+}\to \ddot{I}•K^{+}$ transition.

62 pages 26 figures