AI 中文总结
该研究构建了S波三全同粒子3→3散射的色散表示，推导单粒子交换驱动的线性积分方程，证明其满足三体幺正性，并给出极点扣除方案以获取三体共振极点的解析结构。
AI 中文摘要
我们针对三个无自旋全同粒子的S波过程，构建了相对论性3→3散射振幅的色散表示。我们选取两粒子子能量而非总能量作为色散变量，该选择使物理色散轮廓免受使总能量色散关系复杂化的运动学割线影响。通过区分两粒子子能量割线与三体割线的不连续性，我们推导出以单粒子交换为驱动项的线性积分方程。我们进一步证明，该解因两体幺正性、解析性及交叉对称性而满足三体幺正性。对于两两相互作用，该表示可改写为等压-旁观者散射所用形式。最后，我们给出轮廓变形及两粒子子系统振幅极点扣除的方案，这些方案将振幅延拓至相邻非物理黎曼面，从而直接获取与三体共振极点相关的解析结构。
英文摘要
We construct a dispersive representation of the relativistic $3\to 3$ scattering amplitude for three identical spinless particles in the $S$-wave. The two-particle subenergy, instead of the total energy, is used as the dispersive variable. This choice keeps the physical dispersive contour free of the kinematical cuts that complicate total-energy dispersion relations. By separating discontinuities across the two-particle subenergy cuts from that across the three-body cut, we derive a linear integral equation with one-particle exchange as the driving term. We further show that the solution satisfies three-body unitarity as a consequence of two-body unitarity, analyticity, and crossing symmetry. For pair-wise interactions, this representation can be rewritten into the form used for isobar-spectator scattering. Finally, we give prescriptions for contour deformation and the subtraction of poles in the two-body subsystem amplitudes, which continue the amplitude onto adjacent unphysical Riemann sheets and thus provide direct access to the analytic structure relevant for three-body resonance poles.
Comments15 pages, 5 figures
