Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2010-12-07
Phys.Rev.D83:045013,2011
Physics
High Energy Physics
High Energy Physics - Theory
16 pages, 4 .pdf figures. v2: version accepted for publication in Physical Review D
Scientific paper
10.1103/PhysRevD.83.045013
We present a steepest descent calculation of the Kallen-Lehmann spectral density of two-point functions involving complex conjugate masses in Euclidean space. This problem occurs in studies of (gauge) theories with Gribov-like propagators. As the presence of complex masses and the use of Euclidean space brings the theory outside of the strict validity of the Cutkosky cut rules, we discuss an alternative method based on the Widder inversion operator of the Stieltjes transformation. It turns out that the results coincide with those obtained by naively applying the cut rules. We also point out the potential usefulness of the Stieltjes (inversion) formalism when non-standard propagators are used, in which case cut rules are not available at all.
Dudal David
Guimaraes Marcelo S.
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