Search for Time-Dependent CP Violation in D^{0}→π^{+}π^{-}π^{0} Decays.

A measurement of time-dependent CP violation in D^{0}→π^{+}π^{-}π^{0} decays using a pp collision data sample collected by the LHCb experiment in 2012 and from 2015 to 2018, corresponding to an integrated luminosity of 7.7  fb^{-1}, is presented. The initial flavor of each D^{0} candidate is determined from the charge of the pion produced in the D^{*}(2010)^{+}→D^{0}π^{+} decay. The decay D^{0}→K^{-}π^{+}π^{0} is used as a control channel to validate the measurement procedure. The gradient of the time-dependent CP asymmetry ΔY in D^{0}→π^{+}π^{-}π^{0} decays is measured to be ΔY=(-1.3±6.3±2.4)×10^{-4}, where the first uncertainty is statistical and the second is systematic, which is compatible with CP conservation.