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

Abstract

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