Abstract
We construct a modified on-shell BCFW recursion relation to derive compact analytic representations of tree-level amplitudes in QED. As an application, we study the amplitudes of a fermion pair coupling to an arbitrary number of photons and give compact formulae for the NMHV and N2MHV case. We demonstrate that the new recursion relation reduces the growth in complexity with additional photons to be exponential rather than factorial.
Highlights
Recent years have seen great progress in our understanding of the underlying structures in gauge theories
A well studied example of this is N = 4 super Yang-Mills (SYM) where a rich structure of symmetries has been uncovered in the planar limit [5, 6]
We consider the polynomial behaviour of tree level amplitudes listed above under large values of the complex parameter used in the BCFW recursion relations
Summary
Recent years have seen great progress in our understanding of the underlying structures in gauge theories. For recent examples see [9,10,11,12,13] Analyses of these tree level amplitudes have demonstrated that additional simplifications occur after one obtains expressions from the ordered case via permutation sums. An example of such simplifications is an improved behaviour of the N = 8 supergravity tree level amplitudes over that of N = 4 SYM amplitudes under large complex deformations of the BCFW shift [14]. In the context of gravity amplitudes Spradlin, Volovich and Wen constructed a recursive system which led to compact expression [22] This system can be interpreted as adding a single propagator term into the Cauchy integral.
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