Searching For CP Violation In J/ψ Decays

Up to present, all of the observations on CP violation, for instance in K, B systems,could be interpreted within the Standard Model (SM). Though SM is successful, it failsto explain the asymmetry of the matter and anti-matter in the universe. It is generallybelieved that SM is only an effective theory and new physics beyond the SM is expected.Particularly interesting possibilities are those processes where SM predicts small CP vio-lation effects. The measurement of the electric dipole moment of elementary particles isvary promising as a place to look for further evidence of CP violation.A stringent limit on the electric dipole moment of neutron (and electron) has beenobtained. But the bound for the electric dipole moments ofΛ,Σ,Ξand other particles arefairly weak. J/ψ→ΛΛˉapplies a good laboratory to measure the electric dipole momentofΛ, dΛand to look for CP violation.In this thesis, CP conservation in J/ψ→ΛΛˉis studied. Using 58 million J/ψevents collected by the BESII detector at the BEPC, the decay channel is analyzed tosearch for CP symmetry violation. The expectation value of a CP-odd observable is mea-sured to be (?0.19±1.11±0.93)×10?2, consistent with that CP is conserved in theprocess. Such a measurement may be used to detect the electric dipole moment ofΛun-der proper theoretical assumption. An upper limit of the electric dipole moment is set tobe 2.4×10?16 e cm at 95% confidence level accordingly.Instead of measuring the expectation value of the CP-odd observable directly, wepropose an indirect method which can significantly improve the statistical sensitivity. Inthis improved method, the electric dipole moment ofΛ, dΛcan be detected by analyzingthe full angular distribution in the decay process J/ψ→ΛΛˉ. Monte Carlo studies showthat an expected upper limit of 0.4×10?16 e cm on dΛcan be obtained based on 104 fullyreconstructed J/ψ→ΛΛˉ,Λ→pπ?,Λˉ→pˉπ+ events. This expected upper limit is abouta factor 4 smaller than the one obtained from the direct experimental search to date. Theresult suggests an unprecedented experimental sensitivity on detecting the electric dipolemoment ofΛcould be reached even with the data sample already collected by BESII.The electric dipole moments ofΣ(orΞ) hyperon, dΣ(or dΞ), can also be detectedby analyzing the full angular distribution in the decay process of J/ψ→Σ0Σˉ0(ΞΞˉ). The dependence of dΣ(or dΞ) on the free parameters describing the angular distributionis studied in detail with a Monte Carlo simulation based on 109 J/ψevents expectedin one year data taking at BESIII. The result shows an expected upper limit with 10?16～10?18 e cm on dΣ(or dΞ) can be achieved depending on the true values of free parameters.A test statistic is proposed to perform the goodness-of-fit test in the unbinned max-imum likelihood fit. Without using a detailed expression of the efficiency function, thetest statistic is found to be strongly correlated with the maximum likelihood function ifthe efficiency function varies smoothly. We point out that the correlation coefficient canbe estimated by the Monte Carlo technique. With the established method, two examplesare given to illustrate the performance of the test statistic.CP violation in J/ψ→γ?? is studied too. J/ψcould decay into, on the one hand,γ?? final state directly. On the other hand, J/ψcould decay intoγwith a resonance Ywhich decays into a pair of ?? finally. The full angular distributions in the two processesare studied. It is shown that the expectation value of CP observable is zero in the latterprocess. The measurement of CP violation in experiment is discussed too.