Spherical contours, IR divergences and the geometry of Feynman parameter integrands at one loop

Abstract

Abstract Spherical contours introduced in [1] translate the concept of “discontinuity across a branch cut” to Feynman parameter space. In this paper, we further explore spherical contours and connect them to the computation of leading IR divergences of 1 loop graphs directly in Feynman parameter space. These spherical contours can be used to develop a Feynman parameter space analog of “Leading Singularities” of loop integrands which allows us to develop a method of determining Feynman parameter integrands without the need to sum over Feynman diagrams in momentum space. Finally, we explore some interesting features of Feynman parameter integrands in N $$ \mathcal{N} $$ = 4 SYM.

Keywords

• 1/N Expansion
• Scattering Amplitudes