Double-soft limits of gluons and gravitons

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 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.

Multi-soft theorems in gauge theory from MHV diagrams

“…This particular case has been considered in [24]. Here, we will derive a simpler result that is in agreement with that of [24] (eq. (109)).…”

“…After a bit of algebra this expression simplifies to One can check that (3.14) is a simpler representation of the double-soft factor of two scalars in a singlet configuration first obtained in [24]. As advertised above, this result scales as 1/δ 2 in the double-soft limit.…”

“…This is no longer true when the multi-soft limit involves gluons of different helicities [24,25]. In this note we will restrict ourselves to the leading term in the 1/δ expansion of the universal multi-soft factor S m .…”

“…(2.12) first obtained in [24,25]. At this point we wish to comment on the effectiveness of the CSW method compared to this of the BCFW method.…”

“…The effect of loop corrections to the soft theorems was also considered in [27][28][29][30][31]. More recently, the double-soft theorems for scalars and fermions have been extended to include the double-soft limits of gluons and gravitons [24,25]. Further studies on the soft limit of the S matrix in gauge theories, gravity and string theory can be found in [36][37][38][39][40][41][42][43][44][45][46].…”