Pion pion dynamics in the sigma model
Pion pion dynamics in the sigma model
复制标题
sigma 模型中的 pion π 动力学
DOI：
10.1103/physrevd.2.1680
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发表时间：
1970
期刊：
影响因子：
--
通讯作者：
B. Lee
中科院分区：
文献类型：
--
作者：
J. Basdevant;B. Lee
我们提出了一个明确的方式来构建振幅，同时满足么正性和电流代数约束。这包括在制定高阶修正拉格朗日产生正确的软π极限树近似。我们考虑π π散射的σ模型，我们计算的微扰级数到二阶。重整化过程保留了部分守恒的轴向量电流条件和电流代数约束。为了对强耦合微扰级数求和，我们使用Padé近似技术。因此，我们的分波振幅满足么正性。产生了ρ和f 0共振，尽管它们在拉格朗日量中不存在。我们的么正振幅满足交叉对称性，达到了很好的精度，显示了结果的一致性。我们的结果与I = 0，s波π π相移的"up-down"解一致，具有很宽的σ共振; I = 2的s波相移是排斥的，与实验符合得很好。
We propose an unambiguous way of constructing amplitudes which satisfy both unitarity and the current-algebra constraints. This consists in working out higher-order corrections on a Lagrangian which produces the correct soft-pion limit in the tree approximation. We consider π π scattering in the σ model, and we compute the perturbation series up to second order. The renormalization procedure preserves the partially conserved axial-vector current condition and the current-algebra constraints at each order. In order to sum the strong-coupling perturbation series, we use the Padé-approximation technique. Thereby, our partial-wave amplitudes satisfy unitarity. The ρ and f 0 resonances are generated, although they were not present in the Lagrangian. Our unitary amplitudes satisfy crossing symmetry to a very good accuracy, showing the consistency of the results. Our results are in agreement with the" up-down" solution of the I= 0, s-wave π π phase shift, with a very broad σ resonance; the I= 2 s-wave phase shift is repulsive, and agrees very well with experiment.