Recursion relations from soft theorems

Abstract

We establish a set of new on-shell recursion relations for amplitudes satisfying soft theorems. The recursion relations can apply to those amplitudes whose additional physical inputs from soft theorems are enough to overcome the bad large-z behaviour. This work is a generalization of the recursion relations recently obtained by Cheung et al for amplitudes in scalar effective field theories with enhanced vanishing soft behaviours, which can be regarded as a special case of those with non-vanishing soft limits. We apply the recursion relations to tree-level amplitudes in various theories, including amplitudes in the Akulov-Volkov theory, amplitudes containing dilatons of spontaneously-broken conformal symmetry.Comment: 21 pages, typos and some statements modified, references adde

Unifying relations for scattering amplitudes

“…Fortunately, an amplitude without large z fall-off can still be on-shell constructible if it has compensating infrared properties like the Adler zero or its generalizations [24,25]. As we will show in section 6, the pions in L · A indeed manifest the Adler zero as a transmutation of the Weinberg soft theorems of gauge theory.…”

“…For a detailed discussion on the single-value projection, see for instance [17] and references there in. In any case, the above claim is understood by the convenient KLT form for closed superstring amplitudes 25) where the KLT kernel is for field theory rather than for string theory [1].…”

Lie-algebraic classification of effective theories with enhanced soft limits

“…While the original works focused mostly on gauge theory, more recently the behavior of scattering amplitudes in nonrenormalizable effective field theories (EFTs) for massless scalars -Nambu-Goldstone (NG) bosons -has attracted considerable attention, see for instance refs. [13][14][15]. In this case, the asymptotic behavior of scattering amplitudes in the limit of zero energy (the soft limit) is of particular interest.…”

Soft bootstrap and effective field theories

“…Other related works on soft bootstrap can be found in Refs. [10][11][12][13][14][15][16][17][18][19][20][21].…”

“…It remains to be seen if this is the case. Another complication arises from the fact that, in general, the 6-pt amplitudes at O(p 6 ) are not soft constructible anymore by simple power counting, as the integrand in Eq (11). does not vanish at z = ∞.…”