Partial Wave Analysis Of J/ψ�'γπ～+π～-π～+π～-

QCD non-Abelian gauge theory predicts that two or more gluons couldform pure gluon bound states------glueball. The discovery of glueball is thedirect evidence for proving the QCD non-Abelian gauge theory's validity. Therefore, the identification and study of glueball is one of the most interesting subjects in physics. Though many studies have been performed in experiments and theory, until now, the existence of glueball has not been confirmed.The thesis is based on the 58 million J/ψ data which are collected by BESII at the Beijing Electron Positron Collider(BEPC). It adopts the partial wave analysis of covariant tensor amplitude to analysis J/ψ → γπ+Ï€-Ï€+Ï€channel. The analysis region is below 2.4GeV. Two concrete methods------global fit and bin-by-bin fit are employed to fit the Ï€+Ï€-Ï€+Ï€- invariant mass. Compared with the results of MARK III collaboration and DM2 collaboration, we considered the other two more decay modes: J/ψ → σσ and J/ψ → f₂( 1270)σ besides J/ψ → ρρ.In the global fit for the invariant mass below 2.4GeV, the dominant component is 0-+, meanwhile, there are some 0++ and 2++ component. 0-+ resonances decay to ρρ. 0++ resonances decay dominantly to aa. 2++ resonances in the low mass region decay dominantly to pp, and those in the high mass region decay dominantly to f₂(1270)ρ, partly to pp and aa.For validating the golbal fit result, we also fit the Ï€+Ï€-Ï€+Ï€- invariant mass by bin-by-bin fit method. The outcome indicates that the result of bin-by-bin fit is consistent with the reslut of global fit.After getting the best result, we wipe off the number of resonances and amplitudes to check the signal significance and change the spin-parity of resonances to check the result of analysis. The outcome shows that the partial wave analysis can distinguish between different spin-pariy. It indicated that our result is correct.Finally, we got the branching ratios of different decay modes after calculating the detection efficiency:Br{J/ip - 70-+ -+ rPP) = (2-63 ± 0.02 ± 0.25) x 10"2, Br{Jfi) -+ 70++ -> 7<7 7pp) = (1.31 ± 0.04 ± 0.14) x 10³, Br{J/if> -* 72++ - /2(1270)a) = (4.34 ± 0.07 ±0.44) x 10'3. We find that there are two 0⁺ resonances near low mass: r?(1405)(M = V T = 61t\lMeV) and t/(1475)(M = 1494+^MeF, T = The mass and width of 7/(1405) are accordant with PDG2004 while the mass and width of 7?(1475) aren't. The reason is statistics is better than BES I. We consider the interference among variant partial waves during our analytic procedure. It different from the other experiment group.It is hard to draw a decisive conclusion whether r;(1440) and the 0⁺ component of mass near 1.7GeV are really glueballs, how many glueball component in 77(1440). We think that much more studies are needed.