Abstract
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}ℂℙk−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=3k=3 but we show how they generalise to arbitrary kk. We have explicit analytic results, for any kk, in the case when soft external states are adjacent.
Highlights
In the case of k = 3, we show that the double soft factor for the next to next to adjacent soft external states factorises into a product of two k = 3 single soft factors for each of the soft external states
We found that in the simultaneous double soft limit leading contribution in case of the adjacent soft external states scales as τ−3(k−1) in the τ → 0 limit
It follows from a simple scaling argument, in the canonical color ordering, that when the soft labels i and j in an amplitude are arranged in such a way that |i − j| ∈ {k, k + 1, · · · n − k + 1} the double soft factor is a product of two single soft factors and it scales as τ−2(k−1)
Summary
Our understanding of the scattering amplitudes has improved manifolds in the last couple of decades. We will study double soft limits of amplitudes in the generalised biadjoint scalar field theory. We will study single and double soft limits of n point amplitudes in the biadjoint scalar field theory. After setting up the notation, we will consider single soft theorem in k = 3 case and analyse collision as well as collinear singularities We generalise these results to arbitrary k. We review the single and double soft limits of biadjoint scalar amplitudes for k = 2 in the CHY formalism. In the resulting lower point amplitude canonical ordering would mean labels are arranged in ascending order of magnitude after omitting the soft particles
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