A new and complete proof of the Landau condition for pinch singularities of Feynman graphs and other integrals
arXiv:2007.04085
Abstract
The Landau equations give a physically useful criterion for how singularities arise in Feynman amplitudes. Furthermore, they are fundamental to the uses of perturbative QCD, by determining the important regions of momentum space in asymptotic problems. Generalizations are also useful. We will show that in existing treatments there are significant gaps in derivations, and in some cases implicit assumptions that will be shown here to be false in important cases like the massless Feynman graphs ubiquitous in QCD applications. In this paper is given a new proof that the Landau condition is both necessary and sufficient for physical-region pinches in the kinds of integral typified by Feynman graphs. The proof's range is broad enough to include the modified Feynman graphs that are used in QCD applications. Unlike many existing derivations, there is no need to use the Feynman parameter method. Some possible further applications of the new proof and its subsidiary results are proposed.
39 pages, 10 figures
References in corpus (4)
- k_T factorization is violated in production of high-transverse-momentum particles in hadron-hadron collisions
- Numerical integration of one-loop Feynman diagrams for N-photon amplitudes
- Ultraviolet divergences and factorization for coordinate-space amplitudes
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Cited by in corpus (7)
- Crossing Symmetry in the Planar Limit
- Kinematic singularities of Feynman integrals and principal A-determinants
- Locally finite two-loop amplitudes for off-shell multi-photon production in electron-positron annihilation
- Bounds on Crossing Symmetry
- Graph complexes and Feynman rules
- Natural Boundaries for Scattering Amplitudes
- Momentum Space Landau Equations Via Isotopy Techniques