Evidence of $$A_{CP}(D^0\rightarrow \pi ^+\pi ^-)$$ implies observable CP asymmetry in the $$D^0\rightarrow \pi ^0\pi ^0$$ decay

Inspired by the recent measurement of $CP$ asymmetry in individual mode on LHCb, we study $D\to \pi\pi$ system isospin and topological analysis. The ratio between penguin tree amplitudes $P/(T+C)$ is found to be greater than two most values relative strong phase. And $D^0\to \pi^0\pi^0$ a potential reveal order $10^{-3}$, which would observed Belle II future. large might understood $t$-channel final-state interaction.