The setting sun diagram with complex external momenta
David Dudal, Duifje Maria van Egmond, Gastao Krein

TL;DR
This paper explores the analytic continuation of Feynman integrals with complex external momenta, focusing on the setting sun diagram in two dimensions, and discusses alternative approaches beyond the traditional Källén-Lehmann representation.
Contribution
It provides an analysis of analytic continuation methods for Feynman integrals with complex momenta, highlighting potential differences from the standard Källén-Lehmann approach.
Findings
Analysis of the setting sun diagram in 2D with real mass
Discussion of alternative continuation methods
Implications for complex mass cases
Abstract
We revisit the issue of analytically continuing Feynman integrals from Euclidean to Minkowski signature, allowing for generic complex momenta. Although this is well-known in terms of the K\"all\'{e}n-Lehmann representation, we consider potential alternative takes on the same problem and discuss how these are not necessarily equivalent to the K\"all\'en-Lehmann integral outcome. We present our analysis for a simple enough case -- the setting sun diagram in with a real mass -- but already with an eye out to the more general case with complex masses which will further complicate matters.
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Taxonomy
TopicsNoncommutative and Quantum Gravity Theories · Black Holes and Theoretical Physics · Algebraic and Geometric Analysis
