多道重子-介子散射中的广义Lüscher公式
Generalized Lüscher Formula in Multi-channel Baryon-Meson Scattering
摘要：
Lüscher公式将弹性散射相移与有限立方盒子中的两粒子能级联系起来。在质心坐标系中，得到了两个无自旋大质量粒子弹性散射的原始公式。本文研究了自旋为1/2的粒子与无自旋粒子的多通道散射。建立了两粒子系统能量与散射矩阵元之间的一般关系。我们首先在质心系和一般运动系中利用量子力学得到了这个关系。然后使用参考文献\cite{Hansen:2012tf}中概述的方法将结果推广到量子场论。我们验证，使用这两种方法获得的结果是等价的，指数抑制在盒子大小的条款。
英文摘要：
Lüscher's formula relates the elastic scattering phase shifts to the two-particle energy levels in a finite cubic box. The original formula was obtained for elastic scattering of two massive spinless particles in the center of mass frame. In this paper, we consider the case for the scattering of a spin 1/2 particle with a spinless particle in multi-channel scattering. A generalized relation between the energy of two particle system and the scattering matrix elements is established. We first obtain this relation using quantum-mechanics in both center-of-mass frame and in a general moving frame. The result is then generalized to quantum field theory using methods outlined in Ref. \cite{Hansen:2012tf}. We verify that the results obtained using both methods are equivalent up to terms that are exponentially suppressed in the box size.
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