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Loop Integrands for Scattering Amplitudes from the Riemann Sphere.

Yvonne Geyer1, Lionel Mason1, Ricardo Monteiro2

  • 1Mathematical Institute, University of Oxford, Woodstock Road, Oxford OX2 6GG, United Kingdom.

Physical Review Letters
|October 3, 2015
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Summary

Researchers developed a new framework for calculating scattering amplitudes in physics using off-shell scattering equations. This method extends to arbitrary loop orders for supergravity and super-Yang-Mills theories.

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Area of Science:

  • Theoretical Physics
  • High Energy Physics
  • String Theory

Background:

  • Scattering equations on the Riemann sphere yield formulas for tree-level gauge theory and gravity amplitudes.
  • A one-loop formula for supergravity amplitudes was conjectured using scattering equations on a torus.

Purpose of the Study:

  • To transform the conjectured one-loop supergravity formula into a Riemann sphere framework.
  • To develop a general method for loop integrands applicable to various theories.

Main Methods:

  • Utilized a residue theorem to convert torus-based formulas to the Riemann sphere.
  • Introduced off-shell scattering equations dependent on loop momentum.

Main Results:

  • Established a framework for loop integrands on the Riemann sphere with broad applications.
  • Derived new one-loop formulas for supergravity and super-Yang-Mills amplitudes.
  • Presented n-gon integrands at one loop.

Conclusions:

  • Off-shell scattering equations naturally extend to arbitrary loop orders.
  • Proposed all-loop integrands for supergravity and planar super-Yang-Mills theory.