论文标题
单位性和不稳定的粒子散射幅度
Unitarity and unstable-particle scattering amplitudes
论文作者
论文摘要
单位性是S-矩阵的基本特性，而其对不稳定颗粒的散射的使用却是微妙的，因为不稳定的颗粒没有出现在渐近状态中。将不稳定的颗粒振幅定义为在适当的复合极处的更高点振幅的残基，我们发现了来自单位性和稳定粒子散射振幅的分析性的2至2不稳定粒子幅度的单位方程。当选择进出状态为复杂的偶联位置时，不稳定的粒子校准方程的形式类似于稳定粒子振幅的形式。特别是，与光学定理一样，我们在动量传递变量的正区域中发现了振幅不连续性的阳性约束。
Unitarity is the fundamental property of the S-matrix while its usage for a scattering of unstable particles has been subtle as unstable particles do not appear in the asymptotic states. Defining unstable-particle amplitudes as residues of a higher-point amplitude at an appropriate complex pole, we find unitarity equations for the 2-to-2 unstable-particle amplitudes from unitarity and analyticity of stable-particle scattering amplitudes. The unstable-particle unitarity equations take a form analogous to those of the stable-particle amplitudes when the in and out states are chosen to be complex-conjugate positions. In particular, as in the optical theorem, we find a positivity constraint on a discontinuity of the amplitudes in a positive region of the momentum transfer variable.
