Near threshold expansion of Feynman diagrams

Abstract

The near threshold expansion of Feynman diagrams is derived from their configuration space representation, by performing all x integrations. The general scalar Feynman diagram is considered, with an arbitrary number of external momenta, an arbitrary number of internal lines and an arbitrary number of loops, in n dimensions and all masses may be different. The expansions are considered both below and above threshold. Rules, giving real and imaginary part, are derived. Unitarity of a sunset diagram with I internal lines is checked in a direct way by showing that its imaginary part is equal to the phase space integral of I particles.

arXiv comment57 pages, 7 figures

References in corpus (6)

• Recurrence Relations for Three-Loop Prototypes of Bubble Diagrams with a Mass
• Threshold and pseudothreshold values of the sunset diagram
• On the evaluation of sunset-type Feynman diagrams
• Threshold expansion of Feynman diagrams within a configuration space technique
• Explicitly symmetrical treatment of three-body phase space
• Laurent series expansion of sunrise-type diagrams using configuration space techniques