Analytic two loop results for selfenergy type and vertex type diagrams with one nonzero mass

Aug, 1998
27 pages
Published in:
  • Nucl.Phys.B 547 (1999) 343-374
e-Print:
Report number:
  • BI-TP-98-20

Citations per year

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Abstract:
For a large class of two-loop selfenergy- and vertex-type diagrams with only one non-zero mass (MM) and the vertices also with only one non-zero external momentum squared (q2q^2) the first few expansion coefficients are calculated by the large mass expansion. This allows to `guess' the general structure of these coefficients and to verify them in terms of certain classes of `basis elements', which are essentially harmonic sums. Since for this case with only one non-zero mass the large mass expansion and the Taylor series in terms of q2q^2 are identical, this approach yields analytic expressions of the Taylor coefficients, from which the diagram can be easily evaluated numerically in a large domain of the complex q2q^2-plane by well known methods. It is also possible to sum the Taylor series and present the results in terms of polylogarithms.
Note:
  • LaTeX, 27 pages + 3 ps figures, uses axodraw.sty, some references revisted
  • 12.15.Lk
  • 13.38.-b
  • 12.38.Bx
  • 11.10.Jj
  • Feynman diagram
  • Two-loop diagram
  • Self-energy and vertex diagram
  • Feynman graph: higher-order
  • propagator
  • renormalization