Theoretical analysis of direct CP violation and differential decay width in $$D^\pm \rightarrow \pi ^\pm \pi ^+\pi ^-$$ D ± → π ± π + π - in phase space around the resonances $$\rho ^0(770)$$ ρ 0 ( 770 ) and $$f_0(500)$$ f 0 ( 500 )

Abstract

We perform a theoretical study on direct CP violation in D ± → π ± π + π − in phase space around the intermediate states ρ 0 (770) and f 0 (500). The possible interference between the amplitudes corresponding to the two resonances is taken into account, and the relative strong phase of the two amplitudes is treated as a free parameter. Our analysis shows that by a properly chosen strong phase, both the CP violation strength and the differential decay width accommodate the experimental results.