Recursion Relations for Tree Amplitudes in Super Gauge Theories

TL;DR

The paper applies BCF/BCFW recursion to four-dimensional N=4 super gauge theory amplitudes, deriving compact tree-level gluon results with helicity structure and extending the method to multi-flavor fermions to reproduce MHV and \overline{MHV} amplitudes. It further computes non-MHV amplitudes involving two fermions and four gluons, finding results equivalent to extended CSW prescriptions and conventional calculations, thereby reinforcing the two complementary approaches. The authors discuss criteria for reference-line choices and the large-$z$ behavior of $A(z)$ to justify the recursion with fermions, highlighting the method's efficiency and broad applicability. Overall, the work provides a robust, elegant extension of BCFW that yields concise, verifiable expressions for complex scattering amplitudes.

Abstract

Using newly proposed BCF/BCFW recursion relations, compact formulas are obtained for tree-level n-gluon amplitudes of helicity structure --++...+. We then make an extension of these recursion relations to include fermions of multi-flavors, from which MHV and \bar{MHV} amplitudes are reproduced. We also calculate non-MHV amplitudes of processes with two fermions and four gluons. Results thus obtained are equivalent to those obtained by extended CSW prescriptions, and those by conventional field theory calculations.

Figures (1)

• Figure 1: Pictorial representation of the recursion relation (2.1). Note that the difference between the terms in the two sums is just the helicity assignment of the internal line. bcf