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

We perform a theoretical study on direct $C P$ violation in $D^\pm\to \pi^\pm \pi^+\pi^- $i n p h a s e s p a c e a r o u n d t h e i n t e r m e d i a t e s t a t e s$ \rho^0(770) $a n d$ 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 properly chosen the strong phase, both the $C P$ violation strength and differential decay width accommodate to the experimental results.

Theoretical analysis of direct $C P$ violation and differential decay width in $D^{\pm} \to π^{\pm} π^{+} π^{-}$ in phase space around the resonances $ρ^{0} (770)$ and $f_{0} (500)$

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Theoretical analysis of direct $C P$ violation and differential decay width in $D^{\pm} \to π^{\pm} π^{+} π^{-}$ in phase space around the resonances $ρ^{0} (770)$ and $f_{0} (500)$

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

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

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Theoretical analysis of direct $C P$ violation and differential decay width in $D^{\pm} \to π^{\pm} π^{+} π^{-}$ in phase space around the resonances $ρ^{0} (770)$ and $f_{0} (500)$

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Theoretical analysis of direct $C P$ violation and differential decay width in $D^{\pm} \to π^{\pm} π^{+} π^{-}$ in phase space around the resonances $ρ^{0} (770)$ and $f_{0} (500)$

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