Small threshold behavior of two loop selfenergy diagrams: Two particle thresholds

The behaviour of two-loop two-point diagrams at non-zero thresholds corresponding to two-particle cuts is analyzed. The masses involved in a cut and the external momentum are assumed to be small as compared to some of the other masses of the diagram. By employing general formulae of asymptotic expansions of Feynman diagrams in momenta and masses, we construct an algorithm to derive analytic approximations to the diagrams. In such a way, we calculate several first coefficients of the expansion. Since no conditions on relative values of the small masses and the external momentum are imposed, the threshold irregularities are described analytically. Numerical examples, using diagrams occurring in the Standard Model, illustrate the convergence of the expansion below the first large threshold.

Note:

28 pages (including 23 pages of text in latex and 5 pages with 6 figures in a separate postcript file) Report-no: INLO-PUB-21/95

11.15.Bt
12.38.Bx
11.10.-z.
02.90+p
Feynman integrals
Two-loop diagrams
Self-energies
Two-particle thresholds
Threshold behaviour
Large mass expansion

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