Abstract
We investigate the tree-level S-matrix in gauge theories and open superstring theory with several soft particles. We show that scattering amplitudes with two or three soft gluons of non-identical helicities behave universally in the limit, with multi-soft factors which are not the product of individual soft gluon factors. The results are obtained from the BCFW recursion relations in four dimensions, and further extended to arbitrary dimensions using the CHY formula. We also find new soft theorems for double soft limits of scalars and fermions in $$ \mathcal{N}=4 $$ and pure $$ \mathcal{N}=2 $$ SYM. Finally, we show that the double-soft-scalar theorems can be extended to open superstring theory without receiving any α′ corrections.
Highlights
Double-soft limits have received a lot of attention in the literature, both in the earlier works [52, 53] and more recently
We show that scattering amplitudes with two or three soft gluons of non-identical helicities behave universally in the limit, with multi-soft factors which are not the product of individual soft gluon factors
It is known that when the soft gluons have identical helicities, the result can be obtained by setting the gluons to be soft one by one, we focus on the non-trivial cases when the soft gluons have different helicities
Summary
We start by considering color-stripped amplitudes in gauge theories with two adjacent gluons taken to be soft. A similar simple calculation shows that if the two gluons have different helicities, the result cannot be given by a product of two single soft factors obtained by taking the gluons to be soft one by one This is the non-trivial case we are interested in, namely we would like to study the amplitude A(1+, 2−, 3, . We will use the CHY formula for pure Yang-Mills tree level scattering amplitudes [39] to derive a further formula for the universal double-soft-gluon factor This result will be valid in any dimension, for any helicity combination of the soft gluons, and it will be manifestly free of unphysical poles. We see that the alternating helicity double soft gluon factor is composed of the product of two single soft gluon factors plus a non-trivial correction
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