Asymptotic behavior of Feynman integrals: Convergent integrals

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Abstract
We present a direct and elementary analysis of the asymptotic behavior of convergent Euclidean Feynman integrals for their leading dependence upon large masses and momenta. We also give a bound on the powers of logarithms which accompany the leading power dependence on these parameters. Our treatment includes the case where massless particles are present. As simple corollaries we rederive the Dyson-Weinberg convergence theorem, the results of Lowenstein and Zimmermann on infrared power-counting rules, as well as Weinberg's result for the large-momentum behavior of Feynman integrals. Beyond these results we derive the asymptotic behavior in large masses which is required for the analysis of the effects of heavy particles on low-energy processes involving only light external particles, such as in the proof of the decoupling theorem, and we treat the case where there are an arbitrary number of mass scales present. Our treatment relies on a new recursive partitioning of momentum space which greatly simplifies the proof of the above theorems.