| Three-particle production plays an important role in hadron physics.The treatment of meson decays into three pions using dispersion relations is a classic subject.In 2012 and2015,F.Niecknig and I.V.Danilkin et al.studied the Dalitz plot ofω→π~+π~-π~0 with dispersion relation.The coefficients of the amplitude polynomial parameterization are calculated with and without considering the corss-channel effect.In 2017,WASA-at-COSY Collaboration completed the analysis of Dalitz plot with about 4.4×10~4 events.However,the statistics is limited and the background level is high,the fitting results are not accurate.In 2018,BESⅢ Collaboration has performed the Dalitz plot analysis ofω→π~+π~-π~0 with about 1.9×10~5 events via/→.And the results shows that the cross-channel effect is not significant.In 2020,JPAC Collaboration revisited the dispersive analysis of the decayω→π~+π~-π~0,and the Dalitz plot parameters are in agreement with the previous measurements by BESⅢ.The Beijing Spectrometer Ⅲ(BESⅢ),operating at the south collision point of the Beijing Electron Positron Collider,is a general purpose detector,which is designed for-charm physics.BESⅢ has collected about 10 billion/events in 2009,2012,2018 and2019,which is the world’s largest statistical/samples.It offers an unique laboratory to study the light hardon physics via/decays,which can help us to test the theoretical models of strong interactions at low energy region.Using a sample of 10 billion/events collected at the BESⅢ detector,a cleanω→π~+π~-π~0 sample was selected via the two-body decay/→.We performed the Dalitz plot analysis ofω→π~+π~-π~0 within the framework of the dispersive theory.In this thesis,We used maximum likelihood fit method to obtain parameter coefficients in the decay amplitude under different cases.The fit results show the parameterizations could provide a good description of data,even without introducing the contributions from high orders in the amplitude.The numerical results were consistent with the theoretical predictions and measurements,especially without including the effect of cross-channel,which indicates the effect of cross-channel is not significant. |
