壳层上无质量粒子三点函数的共线性约束以及允许-禁止的$n+1$点函数的含义
Collinearity constraints for on-shell massless particle three-point functions, and implications for allowed-forbidden $n+1$-point functions
摘要：
一个简单的共线性论证意味着无质量粒子螺旋度三点函数$h_1, h_2, h_3$与相应的实值四动量$k_1, k_2, k_3$被视为所有输入或所有输出（即，$k_1 +k_2 +k_3=0$），通过螺旋度守恒消失，除非$h_1+h_2+h_3=0$。当任何一个具有四动量$k$的粒子离开质量壳层时，这个约束不再适用;当$h_1+h_2+h_3\neq 0$在壳层上时，禁戒振幅可以是非零的离壳层，但是当$k$接近质量壳层时，禁戒振幅与$k^2$成比例地消失。当壳上禁止振幅耦合到允许的$n$点振幅以形成$n+1$点函数时，禁止振幅中的该$k^2$因子抵消传播子中的$k^2$，导致在$k^2=0$处没有极点的$n+1$点函数。我们与我们的结果为实值四动量相应的选择规则，已在壳层上的文献中推导出复杂的四动量。
英文摘要：
A simple collinearity argument implies that the massless particle three-point function of helicities $h_1, h_2, h_3$ with corresponding real-valued four-momenta $k_1, k_2, k_3$ taken as all incoming or all outgoing (i.e., $k_1 +k_2 +k_3=0$), vanishes by helicity conservation unless $h_1+h_2+h_3=0$. When any one particle with four-momentum $k$ is off mass shell, this constraint no longer applies; a forbidden amplitude with $h_1+h_2+h_3\neq 0$ on-shell can be nonzero off-shell, but vanishes proportionally to $k^2$ as $k$ approaches mass shell. When an on-shell forbidden amplitude is coupled to an allowed $n$-point amplitude to form an $n+1$ point function, this $k^2$ factor in the forbidden amplitude cancels the $k^2$ in the propagator, leading to a $n+1$-point function that has no pole at $k^2=0$. We relate our results for real-valued four-momenta to the corresponding selection rules that have been derived in the on-shell literature for complexified four-momenta.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
