Theoretical analysis of direct CP violation and differential decay width in D±→π±π+π- in phase space around the resonances ρ0(770) and f0(500)

We perform a theoretical study on direct CP violation in D±→π±π+π- in phase space around the intermediate states ρ0(770) and f0(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