Abstract
The double-soft limit of gluon and graviton amplitudes is studied in four dimensions at tree level. In general this limit is ambiguous and we introduce two natural ways of taking it: a consecutive double-soft limit where one particle is taken soft before the other and a simultaneous limit where both particles are taken soft uniformly. All limits yield universal factorisation formulae which we establish by BCFW recursion relations down to the subleading order in the soft momentum expansion. These formulae generalise the recently discussed subleading single-soft theorems. While both types of limits yield identical results at the leading order, differences appear at the subleading order. Finally, we discuss double-scalar emission in $$ \mathcal{N}=4 $$ super Yang-Mills theory. These results should be of use in establishing the algebraic structure of potential hidden symmetries in the quantum gravity and Yang-Mills S-matrix.
Highlights
Form is strongly constrained by gauge and Poincare symmetry [18, 19]
All limits yield universal factorisation formulae which we establish by BCFW recursion relations down to the subleading order in the soft momentum expansion
Interesting universal double-soft theorems were established. In summary these results indicate that (i) double-soft limits of massless particles exhibit universal behaviour going beyond the single-soft theorems, and (ii) that the doublesoft limits have the potential to exhibit the algebraic structure of underlying hidden symmetries of the S-matrix
Summary
We start from an amplitude of n + 1 particles with momenta p1 to pn+1 and take the momentum of the first particle to be soft by setting p1 = δ1q1 and expanding the√amplitude iλnp1p=ow√erδs1 of δ1 λq1 . In order to keep the notation compact, we will use λq1 ≡ λ1 ≡ |1 and λq1 ≡ λ1 ≡ |1] for the soft particle and λpa ≡ λa ≡ |a and λpa ≡ λa ≡ |a] for the hard ones a = 2, . . . , n + 1.
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