On the tree-level structure of scattering amplitudes of massless particles

Abstract

We provide a new set of on-shell recursion relations for tree-level scattering amplitudes, which are valid for any non-trivial theory of massless particles. In particular, we reconstruct the scattering amplitudes from (a subset of) their poles and zeroes. The latter determine the boundary term arising in the BCFW-representation when the amplitudes do not vanish as some momenta are taken to infinity along some complex direction. Specifically, such a boundary term can be expressed as a sum of products of two on-shell amplitudes with fewer external states and a factor dependent on the location of the relevant zeroes and poles.This allows us to recast the amplitudes to have the standard BCFW-structure, weighted by a simple factor dependent on a subset of zeroes and poles of the amplitudes. We further comment on the physical interpretation of the zeroes as a particular kinematic limit in the complexified momentum space. The main implication of the existence of such recursion relations is that the tree-level approximation of any consistent theory of massless particles can be fully determined just by the knowledge of the corresponding three-particle amplitudes.xxxxx

Investigations into light-front interactions for massless fields (I): non-constructibility of higher spin quartic amplitudes

“…4 BCFW constructibility of flat space higher spin theory in relation to quartic interactions has also been discussed in [13,14] based on [10,11]. 5 It should perhaps be pointed out that the considerations in the present paper are entirely within classical field theory.…”

“…The constructibility assumption -in the sense that quartic amplitudes can be reconstructed from the cubic interaction vertices only -made in BCFW derivations of the quartic higher spin amplitude [10,11] (for a review from a light-front perspective, 2 As far as I'm aware of, there are other groups working on this problem at the present time. This is very good and hopefully we will be able to settle the question (through independent but related efforts) about the existence of consistent quartic interactions in the near future.…”

“…A special approach to quartic amplitudes for massless fields has been investigated by Benincasa and Cachazo [10] and Benincasa and Conde [11,25] in order to map out the consistent interactions among higher and lower spin particles. They use BCFW [26,27] recursion to build quartic tree amplitudes out of cubic amplitudes.…”

Form factor and boundary contribution of amplitude

“…However this assumption is not always true, for example, it fails in the theories involving only scalars and fermions or under the "bad" momentum deformation. Many solutions have been proposed (by auxiliary fields [41,42], analyzing Feynman diagrams [43][44][45], studying the zeros [46][47][48], the factorization limits [49], or using other deformation [50][51][52]) to deal with the boundary contribution in various situations. Most recently, a new multi-step BCFW recursion relation algorithm [53][54][55] is proposed to detect the boundary contribution through certain poles step by step.…”

Higher-spin fermionic gauge fields and their electromagnetic coupling

“…The latter seem promising for the systematic search of consistent interactions of massless higher-spin particles in 4D Minkowski space [64][65][66][67].…”