The propagator seagull: general evaluation of a two loop diagram

Abstract

We study a two loop diagram of propagator type with general parameters through the Symmetries of Feynman Integrals (SFI) method. We present the SFI group and equation system, the group invariant in parameter space and a general representation as a line integral over simpler diagrams. We present close form expressions for three sectors, each with three or four energy scales, for any spacetime dimension $d$ as well as the $ϵ$ expansion. We determine the singular locus and the diagram's value on it.

Comments: 33 pages. v3: The published version - includes the $ϵ$ expansion for the four energy scales sector