Direct evaluation of the d=2 setting sun diagram with a priori complex external momenta disagrees with the Kallen-Lehmann spectral continuation, so complex momenta should be inserted only after performing the integral.
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The setting sun diagram with complex external momenta
Direct evaluation of the d=2 setting sun diagram with a priori complex external momenta disagrees with the Kallen-Lehmann spectral continuation, so complex momenta should be inserted only after performing the integral.