We study double soft theorem for the generalised biadjoint scalar field theory whose amplitudes are computed in terms of punctures on $\mathbb{CP}^{k-1}$. We find that whenever the double soft limit does not decouple into a product of single soft factors, the leading contributions to the double soft theorems come from the degenerate solutions, otherwise the non degenerate solutions dominate. Our analysis uses the regular solutions to the scattering equations. Most of the results are presented for $k=3$ but we show how they generalise to arbitrary $k$. We have explicit analytic results, for any $k$, in the case when soft external states are adjacent.

中文翻译：

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广义双联标量幅值的双软定理

我们研究了广义双联标量场理论的双软定理，其幅值是根据$ \ mathbb {CP} ^ {k-1} $上的穿孔来计算的。我们发现，只要双软极限不解耦为单个软因子的乘积，对双软定理的主要贡献就来自退化解，否则非退化解将占主导。我们的分析对散射方程使用常规解。大部分结果以$ k = 3 $表示，但我们展示了它们如何推广到任意$ k $。对于软外部状态相邻的情况，对于任何$ k $，我们都有明确的分析结果。