Analytic Properties of Triangle Feynman Diagrams in Quantum Field Theory

Abstract

We discuss dispersion representations for the triangle diagram $F(p_1^2,p_2^2,q^2)$, the single dispersion representation in $q^2$ and the double dispersion representation in $p_1^2$ and $p_2^2$, with special emphasis on the appearance of the anomalous singularities and the anomalous cuts in these representations.

13 pages, Lecture given at Helmholtz - DIAS International Summer School "Quantum Field Theory at the Limits: from Strong Fields to Heavy Quarks" 22 July - 2 August 2019, Dubna, Russia. Based on arXiv:hep-ph/0610330

References in corpus (4)

• Cusps in K --> 3 pi decays
• Dispersion relations for ${\gamma }^{\ast }{\gamma }^{\ast }\to \pi \pi$: helicity amplitudes, subtractions, and anomalous thresholds
• Dispersion representations and anomalous singularities of the triangle diagram
• Tetraquark and two-meson states at large $N_{\mathrm{c}}$