Abstract
In this work we employ the MHV technique to show that scattering amplitudes with any number of consecutive soft particles behave universally in the multi-soft limit in which all particles go soft simultaneously. After identifying the diagrams which give the leading contribution we give the general rules for writing down compact expressions for the multi-soft factor of m gluons, k of which have negative helicity. We explicitly consider the cases where k equals 1 and 2. In N =4 SYM, the multi-soft factors of 2 scalars or 2 fermions forming a singlet of SU(4) R-symmetry, and m-2 positive helicity gluons are derived. The special case of the double-soft limit gives an amplitude whose leading divergence is 1/\delta^2 and not 1/\delta as in the case of 2 scalars or 2 fermions that do not form a singlet under SU(4). The construction based on the analytic supervertices allows us to obtain simple expressions for the triple-soft limit of 1 scalar and 2 positive helicity fermions, as well as for the quadrapole-soft limit of 4 positive helicity fermions, in a singlet configuration.
Highlights
After reviewing the scalar graph approach based on the analytic supervertices of the theory, we proceed to consider the multi-soft limit of 2 scalars or 2 fermions forming a singlet under the SU(4) R-symmetry group and m − 2 positive helicity gluons
In this present work we employ the MHV technique to show that scattering amplitudes with any number of consecutive soft particles behave universally in the multi-soft limit when all particles go soft simultaneously
After identifying the diagrams which give the leading contribution we give the general rules from which one can immediately write down compact expressions for m gluons, k of which are negative helicity ones
Summary
One way to obtain compact expressions for purely gluonic amplitudes with any number of particles at tree level is by employing the CSW formalism [50]. We show how one can use this technique to get compact expressions for the multi-soft functions multiplying the “hard” amplitude when any number of adjacent gluons are taken soft simultaneously, namely pi = δqi,. When all these gluons are of the same helicity one can show that the multi-soft factor is the product of m single soft factors as if the particles were taken soft one by one. In this note we will restrict ourselves to the leading term in the 1/δ expansion of the universal multi-soft factor Sm. The first step consists in identifying the set of MHV diagrams which contribute in the soft limit. As we will see only a limited number of MHV diagrams contribute in the soft limit (2.1)
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