Theoretical analysis of direct CPCP violation and differential decay width in D±→π±π+π−D^\pm\to \pi^\pm \pi^+\pi^- in phase space around the resonances ρ0(770)\rho^0(770) and f0(500)f_0(500)

We perform a theoretical study on direct $CP$ violation in $D^\pm\to \pi^\pm \pi^+\pi^-$ in phase space around the intermediate states $\rho^0(770)$ 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 properly chosen the strong phase, both the $CP$ violation strength and differential decay width accommodate to the experimental results.Comment: 15 pages, 5 figure

Stability of Phase-modulated Quantum Key Distribution System

Phase drift and random fluctuation of interference visibility in double unbalanced M-Z QKD system are observed and distinguished. It has been found that the interference visibilities are influenced deeply by the disturbance of transmission fiber. Theory analysis shows that the fluctuation is derived from the envioronmental disturbance on polarization characteristic of fiber, especially including transmission fiber. Finally, stability conditions of one-way anti-disturbed M-Z QKD system are given out, which provides a theoretical guide in pragmatic anti-disturbed QKD.Comment: 9 pages, 3 figue