Cross Section Evaluation by Spinor Integration I: The massless case in 4D

Abstract

To get the total cross section of one interaction from its amplitude $\mathcal{M}$, one needs to integrate $|\mathcal{M}{|}^2$ over phase spaces of all out-going particles. Starting from this paper, we will propose a new method to perform such integrations, which is inspired by the reduced phase space integration of one-loop unitarity cut developed in the last few years. The new method reduces one constrained three-dimension momentum space integration to an one-dimensional integration, plus one possible Feynman parameter integration. There is no need to specify a reference framework in our calculation, since every step is manifestly Lorentz invariant by the new method. The current paper is the first paper of a series for the new method. Here we have exclusively focused on massless particles in 4D. There is no need to carve out a complicated integration region in the phase space for this particular simple case because the integration region is always simply $[0,1]$.

Comments: 28 pages, 1 figure; further comments and references added; Appendix B added