| Beijing Spectrometer(BES â…¢)has collected data samples at several different energy points,such as J/ψ,ψ(2S),ψ(3770)and ψ(4040).And continuum data at3.650GeV were also collected.All these data samples can be used to study the physical topics at Ï„-charm energy region.In this thesis,we introduce measurements of the branching fractions for D+s→η’Ï+and Ds+→η’X.Based on a sample of0.482fb-1data taken at (?)s=4.009GeV, we study the D+sD-s pairs decaying fromψ(4040).With the "single" tag method,we measured B(D+s+→η’Ï+)=(5.6±1.4)%ï¼›with "double tag" method,we measuredå¬(D+s→η’X)=(9.1士2.0±0.5)%.Our measured B(Ds+→p+)is much d-ifferent from the world average(12.5±2.2)%,and our measured B(D+s→η’X)is consistent with the world average(11.7±1.8)%within uncertainty.Based on our measured B(D+s→η’Ï+)and the fractions of other D+s modes with η’ measured by CLEO,we get B(η’K+)+B(η’π+)+B(η’Ï+)+)+B(η’l+νl)=(11.7±1.3)%(exclusive method),which is consistent with the inclusively measured B(D+s→η’X)within er-ror.This analysis resolves the puzzle in PDG:the world averages of B(Ds+→η’X) obtained with inclusive and exclusive method are not consistent. And,the measure-ment is important for testing the theories relevant with Ds decays,and also is helpful for understanding the mixing of η and η’.In addition,this thesis reports a study on the strong phase difference δKÏ€ between D00→K-Ï€+and D0→K-Ï€-+.With the world’s largest ψ(3770)data sample taken at (?)=3.773GeV,we determined the most precise result of δKÏ€ in the world using the quantum coherence between pair-produced D0and D0in ψ(3770)→D0D0.The result is very important for measuring the mixing of D0and D0,and helpful for testing the unitaritv of CKM matrix. |