One-loop calculations in the chirality-flow formalism

Abstract

In a few recent papers we introduced the chirality-flow formalism, which builds on the spinor-helicity formalism, but incorporates the Fierz identity into the Feynman rules. Calculations at tree level are thereby trivial, often to the extent that it is possible to immediately write down a tree-level Feynman diagram in terms of spinor inner products. This simplification persists in tree-level computer implementations, giving very sizable speedups. In the present paper, we argue that there is also a significant simplification of the Lorentz structure at the one-loop level when using the four-dimensional formulation of the four-dimensional helicity scheme. As at tree level, the gauge reference vector for external gauge bosons, and the simplified Lorentz structure lead to significant shortening of the calculations. Additionally, we find that the possible terms in a tensor decomposition of loop integrals are highly constrained, and therefore the tensor reduction procedure is simplified. Published by the American Physical Society 2024