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Analytic Structure of Three-Mass Triangle Coefficients

N. E. J. Bjerrum-Bohr, David C. Dunbar, Warren B. Perkins

Abstract

``Three-mass triangles'' are a class of integral functions appearing in one-loop gauge theory amplitudes. We discuss how the complex analytic properties and singularity structures of these amplitudes can be combined with generalised unitarity techniques to produce compact expressions for three-mass triangle coefficients. We present formulae for the N=1 contributions to the n-point NMHV amplitude.

Analytic Structure of Three-Mass Triangle Coefficients

Abstract

``Three-mass triangles'' are a class of integral functions appearing in one-loop gauge theory amplitudes. We discuss how the complex analytic properties and singularity structures of these amplitudes can be combined with generalised unitarity techniques to produce compact expressions for three-mass triangle coefficients. We present formulae for the N=1 contributions to the n-point NMHV amplitude.

Paper Structure

This paper contains 11 sections, 77 equations.

Table of Contents

  1. Introduction
  2. Organisation of Amplitudes
  3. Singularity Structure of Six-Point Three-Mass Triangles
  4. Infra-Red Singularities
  5. Spurious Singularities
  6. Analytic evaluation of the Three-Mass Triangle Coefficients
  7. Canonical Forms
  8. $n$-Point NMHV ${\cal N}=1$ Results
  9. Beyond NMHV and ${\cal N}=0$
  10. Conclusions
  11. Acknowledgments