Abstract
In a recent paper we introduced the chirality-flow formalism, a method for simple and transparent calculations of Feynman diagrams based on the left- and right-chiral mathfrak {sl}(2,mathbb {C}) nature of spacetime. While our previous work focused on massless QED and QCD at tree-level, we here extend the chirality-flow formalism to the full (tree-level) Standard Model, including massive particles and electroweak interactions – for which the W-interaction simplifies elegantly due to its chiral nature. We illustrate how values of Feynman diagrams can be immediately written down with some representative examples.
Highlights
In a recent paper [1] we introduced the chirality-flow formalism – a flow-like method for treating the Lorentz structure of scattering amplitudes – together with its tree-level Feynman rules in massless QED and QCD
For physics beyond the Standard Model, we note that it is possible to use chirality-flow to describe any theory for which the Lorentz structure can be written down in terms of momenta, the (Minkowski) metric, Dirac (Pauli) matrices, massless Weyl spinors, and polarization vectors
This vertex enters in the Standard Model only at loop level, but we include it here to complete the list of Standard Model Lorentz structures
Summary
In a recent paper [1] we introduced the chirality-flow formalism – a flow-like method for treating the Lorentz structure of scattering amplitudes – together with its tree-level Feynman rules in massless QED and QCD. This method builds on the spinor-helicity formalism [2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17] and is inspired by the color-flow decomposition of the color structure of gluons into fundamental and anti-fundamental representations [18,19,20] It decomposes the Lorentz structure of spin-one bosons into the dotted and undotted left- and right-chiral fields of the Weyl-van-der-Waerden formalism [21,22,23,24,25,26,27,28,29], denoted by dotted and undotted lines respectively, and corresponding to the two sl(2, C) copies of spacetime.
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