Abstract
We take a fresh look at Feynman diagrams in the spinor-helicity formalism. Focusing on tree-level massless QED and QCD, we develop a new and conceptually simple graphical method for their calculation. In this pictorial method, which we dub the chirality-flow formalism, Feynman diagrams are directly represented in terms of chirality-flow lines corresponding to spinor inner products, without the need to resort to intermediate algebraic manipulations.
Highlights
For diagrams or amplitudes in the spinor-helicity formalism, compact analytic expressions exist in the form of the Parke–Taylor formula and other maximallyhelicity-violating (MHV) amplitudes [8,52,53,54,55]
We take a fresh look at Feynman diagrams in the spinor-helicity formalism in massless QED and QCD
In this paper we have presented a new graphical formalism for calculating massless QED and QCD Feynman diagrams
Summary
As a warm-up, let us start with considering a well-known example of a flow-like representation in the context of SU(N ) scattering amplitudes – color flow (with N colors). In the color-flow formalism [3,19,20,28,32] the color factors of Feynman rules are converted into color-flow rules. Color indices in the adjoint representation of SU(N ) are thereby converted to pairs of color indices, one in the fundamental representation and one in the antifundamental representation, and color factors are given by Kronecker δ’s, connecting the fundamental index of one parton to the antifundamental index of another parton. We can write the Fierz identity for the SU(N ) generators tiaj tkal
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