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本文从解析性和么正性出发,对具有共振行为的π-π散射分波振幅的形式作了普遍的讨论。理论中包含了一个标志与Breit-Wigner共振形式偏离的函数F(l)I)(v),当F(l)I)(v)=1时,振幅恰好具有Breit-Wigner共振形式。具体计算表明,这个函数与1有一定的偏离。利用ND-1方法、交叉对称性、ρ与f0的Bootstrap近似,将所得到的振幅与-90的共振解。计算中考虑了非弹性过程和负半轴色散积分的贡献。计算结果得到,对于J=1,I=1态,vR=6.4,Г1=0.12;对于J=2,I=0态,v(R2)=20,Г2=0.016。这相当于mρ=762MeV,mf0=1283MeV,ρ的半宽度约为45MeV。它们与目前的实验数据是很好符合的。From the requirements of analyticity and unitarity, the resonance behaviours of the partial wave amplitudes for π-π scattering are discussed in general. The theory involves a function F(l)I)(v), which indicates deviation from the Breit-Wigner type resonance formula. When F(l)I)(v)=1, the amplitude has exactly the Breit-Wigner form. Further investigation shows that the function F(l)I)(v) in general deviates from 1. By use of the ND-1 method, the crossing symmetry and the ρ- and f0-bootstrap approximation, by comparing with the integral expression of the partial wave amplitude for the interval -90 are calculated. The method takes into account both the contributions of the inelastic process and the dispersion integral of the negative interval. The calculation gives v(R1)=6.4,Г1=0.12 for the J=1, I=1 state and v(R2)=20, Г2=0.016 for the J=2, I=0 state. These results correspond to a mass of 762 MeV and a half-width of about 45 MeV for the ρ meson, and a mass of 1283 MeV for the f0 meson. They are in good agreement with recent experimental data.
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