Double-Cut of Scattering Amplitudes and Stokes' Theorem
arXiv:0905.2909 · doi:10.1016/j.physletb.2009.06.033
Abstract
We show how Stokes' Theorem, in the fashion of the Generalised Cauchy Formula, can be applied for computing double-cut integrals of one-loop amplitudes analytically. It implies the evaluation of phase-space integrals of rational functions in two complex-conjugated variables, which are simply computed by an indefinite integration in a single variable, followed by Cauchy's Residue integration in the conjugated one. The method is suitable for the cut-construction of the coefficients of 2-point functions entering the decomposition of one-loop amplitudes in terms of scalar master integrals.
7 pages, 1 figure; typos corrected, references added, style changed; version accepted by PLB
References in corpus (17)
- Reducing full one-loop amplitudes to scalar integrals at the integrand level
- An Automated Implementation of On-Shell Methods for One-Loop Amplitudes
- Direct extraction of one-loop integral coefficients
- Full one-loop amplitudes from tree amplitudes
- A Numerical Unitarity Formalism for Evaluating One-Loop Amplitudes
- D-dimensional unitarity cut method
- Direct Extraction Of One Loop Rational Terms
- S@M, a Mathematica Implementation of the Spinor-Helicity Formalism
- On Triple-Cut of Scattering Amplitudes
- Unitarity Cuts with Massive Propagators and Algebraic Expressions for Coefficients
- Numerical Evaluation of Six-Photon Amplitudes
- Integral Coefficients for One-Loop Amplitudes
- Closed-Form Decomposition of One-Loop Massive Amplitudes
- Polynomial Structures in One-Loop Amplitudes
- Analytic Structure of Three-Mass Triangle Coefficients
- One-loop Integral Coefficients from Generalized Unitarity
- One-Loop Gluonic Amplitudes from Single Unitarity Cuts