Studies of the resonance structure in $D^0\to K^{\mp }\ddot{I}{€}^{\pm }\ddot{I}{€}^{\pm }\ddot{I}{€}^{\mp }$ decays

Abstract

Amplitude models are constructed to describe the resonance structure of $D^0\to K^{-}\ddot{I}{€}^{+}\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ and $D^0\to K^{+}\ddot{I}{€}^{-}\ddot{I}{€}^{-}\ddot{I}{€}^{+}$ decays using $pp$ collision data collected at centre-of-mass energies of 7 and 8 TeV with the LHCb experiment, corresponding to an integrated luminosity of $3.0{\mathrm{fb}}^{-1}$. The largest contributions to both decay amplitudes are found to come from axial resonances, with decay modes $D^0\to a_1(1260{)}^{+}{K}^{-}$ and $D^0\to K_1(1270/1400{)}^{+}\ddot{I}{€}^{-}$ being prominent in $D^0\to K^{-}\ddot{I}{€}^{+}\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ and $D^0\to K^{+}\ddot{I}{€}^{-}\ddot{I}{€}^{-}\ddot{I}{€}^{+}$, respectively. Precise measurements of the lineshape parameters and couplings of the $a_1(1260{)}^{+}$, $K_1(1270{)}^{-}$ and $K(1460{)}^{-}$ resonances are made, and a quasi model-independent study of the $K(1460{)}^{-}$ resonance is performed. The coherence factor of the decays is calculated from the amplitude models to be $R_{K3\ddot{I}€}=0.459\pm 0.010(\mathrm{stat})\pm 0.012(\mathrm{syst})\pm 0.020(\mathrm{model})$, which is consistent with direct measurements. These models will be useful in future measurements of the unitary-triangle angle ${\hat{I}}^3$ and studies of charm mixing and $CP$ violation.

All figures and tables, along with any supplementary material and additional information, are available at https://cern.ch/lhcbproject/Publications/p/LHCb-PAPER-2017-040.html