2003/07/08 by Stephen P. Martin · 1 citation
Physics and Astronomy · #hep-ph
paper · pdf · doi:10.1103/physrevd.68.075002
published as Phys.Rev.D68:075002,2003 · 17 pages, LaTeX, uses revtex4 and axodraw.sty
arxiv created 2003/07/08 · arxiv updated 2014/11/17
I study the Feynman integrals needed to compute two-loop self-energy functions for general masses and external momenta. A convenient basis for these functions consists of the four integrals obtained at the end of Tarasov's recurrence relation algorithm. The basis functions are modified here to include one-loop and two-loop counterterms to render them finite; this simplifies the presentation of results in practical applications. I find the derivatives of these basis functions with respect to all squared-mass arguments, the renormalization scale, and the external momentum invariant, and express the results algebraically in terms of the basis. This allows all necessary two-loop self-energy integrals to be efficiently computed numerically using the differential equation in the external momentum invariant. I also use the differential equations method to derive analytic forms for various special cases, including a four-propagator integral with three distinct non-zero masses.