Landau Analysis in Momentum Space with Massless Particles: an Amuse Bouche

TL;DR

This paper extends Landau analysis methods from massive to massless Feynman integrals in momentum space, demonstrating how singularities and integral behaviors change with different propagator mass configurations.

Contribution

It introduces a generalization of Landau analysis techniques to massless integrals, including the use of resolution of singularities for arbitrary propagator mass configurations.

Findings

Methods from Landau analysis are successfully generalized to massless integrals.

Resolution of singularities helps predict integral behavior with massless propagators.

Examples illustrate how integral properties change with different mass configurations.

Abstract

We illustrate how methods from Landau analysis that have been developed for studying the properties of massive Feynman integrals in momentum space can be generalized to massless integrals. We consider integrals with both massive and massless propagators in arbitrary dimensions, paying attention to square root branch points. By focusing on a number of well-chosen examples, we show how resolution of singularities (via blow-ups or complex structure deformation) can be used to predict how the behavior of these integrals is modified as different numbers of propagators are chosen to be massless.