Determination of $U$-spin breaking parameters with an amplitude analysis of the decay $D^0\to K_{\text{S},\text{L}}^0{\pi }^{+}{\pi }^{-}$

Abstract

We perform a simultaneous amplitude analysis of the decays $D^0\to K_{\text{S}}^0{\pi }^{+}{\pi }^{-}$ and $D^0\to K_{\text{L}}^0{\pi }^{+}{\pi }^{-}$ using an $e^{+}{e}^{-}$ collision data sample, corresponding to an integrated luminosity of $20.3{\text{fb}}^{-1}$, collected at the centre-of-mass energy of $3.773\text{GeV}$ with the BESIII detector. This study, based on a significantly larger dataset than that used in previous work, presents an updated measurement of the complex $U$-spin breaking parameters ($\hat{\rho }$) associated with various $CP$ eigenstate resonant modes mediating the three-body decays. The magnitudes of the $\hat{\rho }$ parameters range from $0.62$ to $4.45$, indicating substantial $U$-spin symmetry breaking. We also report the resonant fit fraction and obtain a model prediction for the average strong-phase parameters over regions of phase space for both decay modes.